Answers to Supplementary Problems

Chapter 1

1. (a) point; (b) line; (c) plane; (d) plane; (e) line; (f) point

2. (a) Image, Image (b) Image, Image, Image, Image (c) Image, Image, Image, Image; (d) F

3. (a) AB = 16; (b) AE = Image

4. (a) 18; (b) 90°; (c) 50°; (d) 130°; (e) 230°

5. (a) ∠CBE; (b) ∠AEB; (c) ∠ABE; (d) ABC, ∠BCD, ∠BED; (e) ∠AED

6. (a) 130°; (b) 120°; (c) 75°; (d) 132°

7. (a) 75°; (b) 40°; (c) or 10Image or 10°20′; (d) 9°11′

8. (a) 90°; (b) 120°; (c) 135°; (d) 270°; (e) 180°

9. (a) 90°; (b) 60°; (c) 15°; (d) 165°

10. (a) Image ⊥ Image and Image ⊥ Image (b) 129°; (c) 102°; (d) 51°; (e) 129°

11. (a) ΔABC, hypotenuse Image, legs Image and Image

ΔACD, hypotenuse Image, legs Image and Image

ΔBCD, hypotenuse Image, legs Image and Image

(b) ΔDAB and ΔABC

(c) ΔAEB, legs Image and Image, base Image, vertex angle ∠AEB

ΔCED, legs Image and Image base Image vertex angle ∠CED

12. (a) Image ≐ Image and ∠PRA ≐ ∠PRB; (b) ∠ABF ≐ ∠CBF; (c) ∠CGA ≐ ∠CGD; (d) Image ≐ Image

13. (a) vert. Image; (b) comp. adj. Image; (c) adj. Image; (d) supp. adj. Image; (e) comp. Image; (f) vert. Image

14. (a) 25°, 65°; (b) 18°, 72°; (c) 60°, 120°; (d) 61°, 119°; (e) 50°, 130°; (f) 56°, 84°; (g) 90°, 90°

15. (a) a + b = 75°, a – b = 21°, a = 48° and b = 27°

(b) a + b = 90°, a = 3b–10°, a = 65° and b = 25°

(c) a + b = 180°, a = 4b + 20°, a = 148° and b = 32°

Chapter 2

1. (a) A is H; (b) P is D; (c) R is S; (d) E is K ; (e) A is G ; (f) triangles are geometric figures; (g) a rectangle is a quadrilateral

2. (a) a = c = f; (b) g = 15; (c) f = a; (d) a = f, a = h, c = h; (e) b = g, b = e, d = e

3. (a) 130; (b) 4; (c) yes; (d) x = 8Image°; (e) y = 15; (f) x = 6; (g) x =±6

4. (a) AC = 12, AE = 11, AF = 15, DF = 9

(b) m∠ADC = 92°, m∠BAE = 68°, m∠FAD = 86°, m∠BAD = 128°

5. (a) AB = DF; (b) AB = AC ; (c) ∠ECA ≐ ∠DCB; (d) ∠BAD ≐ ∠BCD

6. (a) If equals are divided by equals, the quotients are equal.

(b) Doubles of equals are equal.

(c) If equals are multiplied by equals, the products are equal.

(d) Halves of equals are equal.

7. (a) If equals are divided by equals, the quotients are equal.

(b) If equals are multiplied by equals, the products are equal.

(c) Doubles of equals are equal.

(d) Halves of equals are equal.

8. (a) Their new rates of pay per hour will be the same. (Add. Post.)

(b) Those stocks have the same value now. (Mult. Post.)

(c) The classes have the same number of pupils now. (Subt. Post.)

(d) 100°C = 212°F (Trans. Post.)

(e) Their parts will be the same length. (Div. Post.)

(f) He has a total of $10,000 in Banks A, B, and C. (Part. Post.)

(g) Their values are the same. (Trans. Post.)

9. (a) Vertical angles are congruent.

(b) All straight angles are congruent.

(c) Supplements of congruent angles are congruent.

(d) Perpendiculars form right angles and all right angles are congruent.

(e) Complements of congruent angles are congruent.

10. In each answer, (H) indicates the hypothesis and (C) indicates the conclusion.

(a) (H) Stars, (C) twinkle.

(b) (H) Jet planes, (C) are the speediest.

(c) (H) Water, (C) boils at 212° Fahrenheit.

(d) (H) If it is the American flag, (C) its colors are red, white, and blue.

(e) (H) If you fail to do homework in the subject, (C) you cannot learn geometry.

(f) (H) If the umpire calls a fourth ball, (C) a batter goes to first base.

(g) (H) If A is B’s brother and C is B’s daughter, (C) then A is C′s uncle.

(h) (H) An angle bisector, (C) divides the angle into two equal parts.

(i) (H) If it is divided into three equal parts, (C) a segment is trisected.

(j) (H) A pentagon (C) has five sides and five angles.

(k) (H) Some rectangles (C) are squares.

(l) (H) If their sides are made longer, (C) angles do not become larger.

(m) (H) If they are congruent and supplementary, (C) angles are right angles.

(n) (H) If one of its sides is not a straight line segment, (C) the figure cannot be a polygon.

11. (a) An acute angle is half a right angle. Not necessarily true.

(b) A triangle having one obtuse angle is an obtuse triangle. True.

(c) If the batter is out, then the umpire called a third strike. Not necessarily true.

(d) If you are shorter than I, then I am taller than you. True.

(e) If our weights are unequal, then I am heavier than you. Not necessarily true.

Chapter 3

1. (a) ΔI ≐ ΔII ≐ ΔIII, SAS; (b) ΔI ≐ ΔIII, ASA; (c) ΔI ≐ ΔII ≐ ΔIII, SSS.

2. (a) ASA; (b) SAS; (c) SSS; (d) SAS; (e) ASA; (f) SAS; (g) SAS; (h) ASA.

3. (a) Image ≐ Image (b) ∠ABD = ∠DBC; (c) ∠1 ≐ ∠4; (d) Image ≐ Image (e) Image ≐ Image ; (f) ∠BAD ≐ ∠CDA

4. (a) ∠1 ≐ ∠3, ∠2 ≐ ∠4, Image ≐ Image (b) Image ≐ Image, Image ≐ Image, ∠B ≐ ∠C;

(c) ∠E ≐ ∠C, ∠A ≐ ∠F, ∠EDF ≐ ∠ABC

5. (a) x = 19, y = 8; (b) x = 4, y = 12; (c) x = 48, y = 12

8. (a) ∠b ≐ ∠d, ∠E ≐ ∠G; (b) ∠A ≐ ∠1 ≐ ∠4, ∠2 ≐ ∠C; (c) ∠1 ≐ ∠5, ∠4 ≐ ∠6, ∠EAD ≐ ∠EDA

9. (a) Image ≐ Image; (b) Image ≐ Image ≐ Image, Image ≐ Image (c) Image ≐ Image, Image ≐ Image, Image ≐ Image

Chapter 4

1. (a) x = 105°, y = 75°; (b) x = 60°, y = 40°; (c) x = 85°, y = 95°; (d) x = 50°, y = 50°;

(e) x = 65°, y = 65°; (f) x = 40°, y = 30°; (g) x = 60°, y = 120°; (h) x = 90°, y = 35°;

(i) x = 30°, y = 40°; (f) x = 80°, y = 10°;(k) x = 30°, y = 150°;(l) x = 85°, y = 95°

2. (a) x = 22°, y = 102°; (b) x = 40°, y = 100°; (c) x = 80°, y = 40°

3. (a) Each angle measures 105°. (b) Each angle measures 70°. (c) Angles measure 72° and 108°.

7. (a) 25; (b) 9; (c) 20; (d) 8

8. (a) 8; (b) 10; (c) 2; (d) 14

10. (a) P is equidistant from B and C. P is on ⊥ bisector of Image.

Q is equidistant from A and B. Q is on ⊥ bisector of Image.

R is equidistant from A, C, and D. R is on ⊥ bisectors of Image and Image.

(b) P is equidistant from and Image and Image P is on bisector of ∠A.

Q is equidistant from Image and Image Q is on bisector of ∠B.

R is equidistant from Image, Image and Image R is on the bisectors of ∠C and ∠D.

11. (a) P is equidistant from Image, Image and Image Q is equidistant from Image and Image and equidistant from A and D. R is equidistant from Image and Image and equidistant from A and D.

(b) P is equidistant from Image and Image and equidistant from B and C. Q is equidistant from A, B, and C.

R is equidistant from Image and Image and equidistant from A and B.

12. (a) x = 50°, y = 110°; (b) x = 65°, y = 65°; (c) x = 30°, y = 100°; (d) x = 51°, y = 112°;

(e) x = 52°, y = 40°; (f) x = 120°, y = 90°

13. (a) x = 55°, y = 125°; (b) x = 80°, y = 90°; (c) x = 56°, y = 68°; (d) x = 100°, y = 30°;

(e) x = 30°, y = 120°; (f) x = 90°, y = 30°

14. (a) 18°, 54°, 108°; (b) 40°, 50°, 90°; (c) 36°, 36°, 108°; (d) 36°, 72°, 108°, 144°; (e) 50°, 75°; (f) 100°, 60°, and 20°

16. (a) Since x = 45, each angle measures 60°.

(b) Since x = 25, x + 15 = 40 and 3x–35 = 40; that is, two angles each measure 40°.

(c) If 2x, 3x, and 5x represent the angles, x = 18 and 5x = 90; that is, one of the angles measures 95°.

(d) If x and 5x–10 represent the unknown angles, x = 21 and 5x–10 = 95; that is, one of the angles measures 95°.

17. (a) 7 st. Image, 30 st. Image; (b) 1620°, 5400°, 180,000°; (c) 30, 12, 27, 202

18. (a) 20°, 18°, 9°; (b) 160°, 162°, 171°; (c) 3, 9, 20, 180; (d) 3, 12, 36, 72, 360

19. (a) 65°, 90°, 95°, 110°; (b) 140°, 100°, 60°, 60°

20. (a) ΔI ≐ ΔIII by hy-leg; (b) ΔI ≐ ΔIII by SAA.

Chapter 5

1. (a) x = 15, y = 25; (b) x = 20, y = 130; (c) x = 20, y = 140

4. (a) ImageEFGH; (b) ImageABCD and EBFD; (c) ImageGHKJ, HILK, GILJ; (d) ImageACHB, CEFH

5. (a) Two sides are congruent and ||. (b) Opposite sides are congruent.

(c) Opposite angles are congruent. (d) Image and Image are congruent and parallel (Image ≐ Image ≐ BC).

6. (a) x = 6, y = 12; (b) x = 5, y = 9; (c) x = 120, y = 30; (d) x = 15, y = 45

7. (a) x = 14, y = 6; (b) x = 18, y = 4Image (c) x = 8, y = 5; (d) x = 3, y = 9

10. (a) x = 5, y = 7; (b) x = 10, y = 35; (c) x = 2Image y = 17Image (d) x = 8, y = 4; (e) x = 25, y = 25;

(f) x = 11, y = 118

13. (a) x = 6, y = 40; (b) x = 3, y = 5Image (c) x = 8Image, y = 22

14. (a) x = 28, y = 25Image; (b) x = 12 (since y does not join midpoints, Pr. 3 does not apply);

(c) x = 19, y = 23Image

15. (a) m = 19; (b) b′= 36; (c) b = 73

16. (a) x = 11, y = 33; (b) x = 32, y = 26; (c) x = 12, y = 36

17. (a) 22Image; (b) 70

18. (a) 21; (b) 30; (c) 14; (d) 26

Chapter 6

5. (a) square; (b) isosceles triangle; (c) trapezoid; (d) right triangle

6. (a) 140°; (b) 60°; (c) 90°; (d) (180–x) °; (e) x°; (f) (90 + x) °

7. (a) 100°; (b) 50°, 80°; (c) 54°, 27°; (d) 45°; (e) 35°; (f) 45°

8. (a) x = 22; (b) y = 6; (c) AB + CD = 22; (d) perimeter = 44; (e) x = 21; (f) r = 14

9. (a) 0; (b) 40; (c) 33; (d) 7

10. (a) tangent externally; (b) tangent internally; (c) the circles are 5 units apart; (d) overlapping

11. (a) concentric; (b) tangent internally; (c) tangent externally; (d) outside each other; (e) the smaller entirely inside the larger; (f) overlapping

13. (a) 40; (b) 90; (c) 170; (d) 180; (e) 2x; (f) 180–x; (g) 2x–2y

14. (a) 20; (b) 45; (c) 85; (d) 90; (e) 130; (f) 174; (g) x; (h) 90–Imagex ; (i) x–y

15. (a) 85; (b) 170; (c) c; (d) 2i; (e) 60; (f) 30

16. (a) 60, 120, 180; (b) 80, 120, 160; (c) 100, 120, 140; (d) 36, 144, 180

17. (a) m∠x = 136°; (b) mImage = 11° (c) m∠x = 130°; (d) m∠y = 126°; (e) m∠x = 110°; mImage = 77°

18. (a) 135°; (b) 90°; (c) (180–x) °; (d) (90 + x) °; (e) 100°; (f) 80°; (g) 55°; (h) 72°

19. (a) 85°; (b) y°; (c) 110°; (d) 95°; (e) 72°; (f) 50°; (g) 145°; (h) 87°

20. (a) 50; (b) 60

21. (a) m Image = 65°, (b) m Image = 90°, m∠y = 55°; (c) m∠x = 37°, m∠y = 50°

22. (a) 19; (b) 45; (c) 69; (d) 90; (e) 125; (f) 167; (g) Imagex ; (h) 180–Imagex ; (i) x + y

23. (a) 110; (b) 135; (c) 180; (d) 270; (e) 180–2x; (f) 360–2x; (g) 2x–2y; (h) 7x

24. (a) 45°; (b) 60°; (c) 30°; (d) 18°

25. (a) m Image = 120°, m∠y = 60°; (b) m∠x = 62°, m∠y = 28°; (c) m∠x = 46°, m∠y = 58°

26. (a) 75°; (b) 75°; (c) 115°; (d) 100°; (e) 140°; (f) 230°; (g) 80°; (h) 48°

27. (a) 85°; (b) 103°; (c) 80°; (d) 72°; (e) 90°; (f) 110°; (g) 130°; (h) 110°

28. (a) m Image = 68°, m∠y = 95°, (b) m∠x = 90°, m∠y = 120°; (c) m∠Image = 34°, m∠Image = 68°

29. (a) 30°; (b) 37°; (c) 20°; (d) 36°; (e) 120°; (f) 130°; (g) 94°; (h) 25°

30. (a) 45°; (b) 75°; (c) 50°; (d) 36 Image°; (e) 90°; (f) 140°; (g) 115°; (h) 45°; (i) 80°

31. (a) 20°; (b) 85°; (c) (180–x) °; (d) (90 + x) °; (e) 90°; (f) 25°; (g) 42°; (h) 120°; (i) 72°; (j) 110°;

32. (a) m Image = 43°, m∠y = 43°, (b) mImage = 190°, m∠y = 55°; (c) m Image = 140°, m∠y = 40°

33. (a) 120°; (b) 150°; (c) 180°; (d) 50°; (e) 22Image (f) 45°

34. (a) m Image = 150°, m Image = 40°; (b) m Image = 190°, m Image = 70°; (c) m Image = 252°, m Image = 108°

35. (a) 25°; (b) 39°; (c) 50°; (d) 30°; (e) 40°; (f) 76°; (g) 45°; (h) 95°; (i) 75°; (j) 120°

36. (a) 74°; (b) 90°; (c) 55°; (d) 60°; (e) 40°; (f) 37°; (g) 84°; (h) 110°; (i) 66°; (j) 98°; (k) 75°; (l) 79°

37. (a) m∠x = 120°, m∠y = 60°; (b) m∠x = 45°, m∠y = 67Image°; (c) m∠x = 36°, m∠y = 72°

38. (a) m Image = 40°, m∠y = 80°; (b) m Image = 45°, m∠y = 67Image °; (c) m∠x = 78°, m∠y = 103°

Chapter 7

1. (a) 4; (b) Image (c) Image (d) Image (e) Image (f) 2; (g) Image (h) Image (i) Image (j) Image (k) 2; (l) Image (m) 20; (n) Image (o) 3

2. (a) 6; (b) Image (c) Image (d) Image (e) 3; (f) Image (g) 2; (n) 250; (i) Image (j) 8; (k) Image (l) Image

3. (a) 2: 3: 10; (b) 12: 6: 1; (c) 5: 2: 1; (d) 1: 4: 7; (e) 4: 3: 1; (f) 8: 2: 1; (g) 50: 5: 1; (h) 6: 2: 1; (i) 8: 2: 1

4. (a) Image (b) 12; (c) Image (d) Image (e) 6; (f) Image (g) Image (h) Image (i) Image (j) 11; (k) Image(1) 60; (m) 3; (n) Image (o) Image(p) 14

5. (a) Image (b) 3c; (c) Image (d) Image (e) Image (f) Image (g) Image (h) Image (i) 1: 4: 10; (j) 3: 2: 1; (k) x2: x : l; (l) 6: 5: 4: 1

6. (a) 5x and 4x, sum = 9x; (b) 9x and x, sum = lOx ; (c) 2x, 5x, and 11x, sum = 18. x ; (d) x, 2x, 2x, 3x, and 7x, sum = 15x

7. (a) 5 x + 4 x = 45, x = 5, 25°; and 20°; (b) 5x + 4x = 90, x = 10, 50°; and 40°;

(c) 5x + 4x = 180, x = 20, 100°; and 80°; (d) 5x + 4x + x = 180, x = 18, 90°; and 72°;

8. (a) 7x + 6x = 91, x = 7, 49°, 42°; and 35°; (b) 7x + 5x = 180, x = 15, 105°, 90°; and 75°

(c) 7x + 3x = 90, x = 9, 63°, 54°; and 45°; (d) Ix + 6x + 5x = 180, x = 10, 70°, 60°; and 50°;

9. (a) 16; (b) 16; (c) ±6; (d) ± 2 Image (e) ±5; (f) 2; (g) Image (h) ±6y

10. (a) 21; (b) 4Image (c) ±6; (d) ± Image (e) 8; (f) ±4; (g) 3; (h) ± Image

11. (a) 15; (b) 3; (c) 6; (d) 2Image; (e) 3Image; (f) 30; (g) 32; (h) 6a

12. (a) 6; (b) 6; (c) 3; (d) 4b; (e) Image; (f) Image; or 3 Image; (g) Image; (h) a Image

13. (a) Image (b) Image (c) Image (d) Image (e) Image

14. (a) Image (b) Image (C) Image (d) Image (e) Image

15. Only (b) is not a proportion since 3(12) ≠ 5(7); that is, 36 ≠ 35.

16. (a) Image (b) Image (c) Image (d) Image (e) Image

17. (a) d; (b) 35; (c) 5 (d) 4

18. (a) 21; (b) Image; (c) 5

19. (a) 16; (b) 6Image (c) 10

20. (a) yes, since Image; (b) no, since Image; (c) yes, since Image

21. (a) 12; (b) 8; (c) 60

22. (a) 15; (b) 15; (c) 6Image

24. (a) 35°; (b) 53°

25. (a) a = 16; (b) b = 15; (c) c = 126

27. (a) ∠ABE ≐ ∠EDC, ∠BAE ≐ ∠DCE (also vert. Image at E)

(b) ∠BAF ≐ ∠FEC, ∠B ≐ ∠D (also ∠EAD ≐ ∠BFA)

(c) ∠A ≐ ∠EDF, ∠F ≐ ∠BCA

(d) ∠A ≐ ∠A, ∠B ≐ ∠C

(e) ∠C ≐ ∠D, ∠CAB ≐ ∠CAD

(f) ∠A ≐ ∠A, ∠C ≐ ∠DBA

28. (a) ∠D ≐ ∠B, ∠AED ≐ ∠FGB ; (b) ∠ADB ≐ ∠ABC, ∠A ≐ ∠A ; (c) ∠ABC ≐ ∠AED, ∠BAE ≐ ∠EDA

29. (a) ∠C ≐ ∠F, Image (b) ∠A ≐ ∠A, Image (c) ∠B ≐ ∠B, Image

30. (a) Image (b) Image (c) Image

32. (a) q = 20; (b) p = 8; (c) b = 7; (d) a = 12; (e) AB = 35; (f) d = 2Image

33. (a) 8; (b) 6; (c) 26Image

34. (a) 42 ft; (b) 66ft

37. (a) 8:5; (b) 3:5; (c) halved (in each case)

38. (a) 15; (b) 60; (c) 25, 35, 40; (d) 4; (e) 6, 3

39. (a) 3: 7; (b) 7: 2; (c) quadrupled; (d) 7

43. (a) 5; (b) 14; (c) 6; (d) 5; (e) 12; (f) 13; (g) 48; (h) 2

44. 30, 18

45. (a) 8; (b) 6; (c) 12; (d) 5; (e) 7; (f) 12; (g) 30; (h); 7Image (i) 5; (j) 8

46. (a) 8; (b) 13; (c) 21; (d) 6; (e) 9; (f) 14; (g) 3; (h) 8

47. (a) a = 4. h = Image; or 2Image; (b) c = 9, h = Image; or 2Image; (c) q = 4 and b = Image; or 4Image; (d) p = 18, h = Image; = 6 Image

48. (a) 25; (b) 39; (c) Image; (d) 10; (e) 7Image

49. (a) b = 16; (b) a = 2Image; (c) a = 8; (d) b = 2 Image; (e) b = 5Image; b = Image

50. (a) 9.12; (b) 10.24; (c) 80.150; (d) 2Image,4Image

51. (a) 41; (b) 5 Image

52. (a) 12; (b) 10 Image; (c) 5 Image

53. All except (h)

54. (a) yes; (b) no, since (2x)2 + (3x)2 ≠ (4x)2

55. (a) 8; (b) 6; (c) Image; (d) 5 Image

56. (a) 15; (b) 2 Image; (c) 6

57. (a) 16; (b) 30; (c) 4Image; (d) 10

58. (a) 10; (b) 12; (c) 28; (d) 15

59. (a) 5; (b) 20; (c) 15; (d) 25

60. (a) 12; (b) 24

61. 12

62. 30

63. (a) 10 and 10Image; (b) 7Image; and 14; (c) 5 and 10

64. (a) 11Image; (b) a Image; (c) 48; (d) 16 Image

65. (a) 25 and 25Image; (b) 35 and 35Image

66. (a) 28, 8Image; (b) 17, 14 Image

67. (a) 17 Image; (b) a Image; (c) 34 Image; (d) 30

68. (a) 20 Image; (b) 40 Image

69. (a) 45, 13 Image; (b) 11, 27 Image; (c) 15 Image, 55

70. 6Image, 5 Image

Chapter 8

1. (a) 0.4226, 0.7431, 0.8572, 0.9998; (b) 0.9659, 0.6157, 0.2756, 0.0349;

(c) 0.0699, 0.6745, 1.4281, 19.0811; (d) sine and tangent; (e) cosine; (f) tangent

2. (a) x = 20°; (b) A = 29°; (c) B = 71°; (d) A′ = 21°; (e) y = 45°; (f) Q = 69°; (g) W = 19°; (h) B′ = 67°

3. (a) 26°; (b) 47°; (c) 69° (d) 8°; (e) 40°; (f) 74° (g) 7° (h) 27°; (i) 80°; (j) 13° since sin x = 0.2200;

(k) 45° since sin x = 0.707; (l) 59° since cos x = 0.5200; (m) 68° since cos x = 0.3750;

(n) 30° since cos x = 0.866; (o) 16° since tan x = 0.2857; (p) 10° since tan x = 0.1732

4. (a) sin A = Image, cos A = Image, tan A = Image, (b) sin A = Image, tan A = Image

Image

5. (a) m∠A = 27°since cos A = 0.8900; (b) m∠A = 58° since sin A = 0.8500;

(c) m∠A = 52° since tan A = 1.2800

6. (a) m∠A = 42°since sin B = 0.6700; (b) m∠B = 74° since cos B 0.2800;

(c) m∠B 68° since tan B = 2.500; (d) m∠B = 30° since tan B = 0.577

8. (a) 23°, 67°; (b) 28°, 62°; (c) 16°, 74°; (d) 10°, 80°

9. (a) x = 188, y = 313; (b) x 174, y = 250; (c) x = 123, y = 182

10. (a) 82 ft; (b) 88 ft

11. 156 ft

12. (a) 2530 ft; (b) 2560 ft

13. (a) 21 in; (b) 79 in

14. 14

15. 16 and 18 in

16. 31 ft

17. 15 yd

18. (a) 1050 ft; (b) 9950 ft

19. 7°

20. 282 ft

21. (a) 81°; (b) 45°

22. (a) 22 ft; (b) 104 ft

23. 754 ft

24. 404 ft

25. (a) 295 ft; (b) 245 ft; (c) 960 ft

26. (a) 234 ft; (b) 343 ft

27. (a) 96 ft; (b) 166 ft

28. 9.1

Chapter 9

1. (a) 99 in2; (b) 3 ft2 or 432 in2; (c) 500; (d) 120; (e) 36 Image; (f) 100 Image; (g) 300; (h) 150

2. (a) 48; (b) 432; (c) 25 Image; (d) 240

3. (a) 7 and 4; (b) 12 and 6; (c) 9 and 6; (d) 6 and 2; (e) 10 and 7; (f) 20 and 8

4. (a) 1296 in2; (b) 100 square decimeters (100 dm2)

5. (a) 225; (b) 12Image (c) 3.24; (d) 64a2; (e) 121; (t) 6Image (g) 9 b2; (h) 32; (i) 40Image (j) 64

6. (a) 128; (b) 72; (c) 100; (d) 49; (e) 400

7. (a) 1600; (b) 400; (c) 100

8. (a) 9; (b) 36; (c) 9 Image; (d) 4Image; (e) Image;Image

9. (a) 2Image (b) 52; (c) 10; (d) 5 Image; (e) 6; (f) 4

10. (a) 16 ft2; (b) 6 ft2 or 864 in2; (c) 70; (d) 1.62 m2

11. (a) 3x2; (b) x2 + 3x ; (c) x2–25; (d) 12x2 + 11 x + 2

12. (a) 36; (b) 15; (c) 16

13. (a) 2Image; (b) 20; (c) 9; (d) 3; (e) 15; (f) 12; (g) 8; (h) 7

14. (a) 11 in2; (b) 3 ft2 (c) 4x–28; (d) 10x2; (e) 2x2 + 18x ; (f) Image(x2–16) ; (g) x2–9

15. (a) 84; (b) 48; (c) 30; (d) 120; (e) 148; (f) 423; (g) 8 Image; (h) 9

16. (a) 24; (b) 2; (c) 4

17. (a) 8; (b) 10; (c) 8; (d) 18; (e) 9Image (f) 12Image (g) 12; (h) 18

18. (a) 25 Image; (b) 36 Image; (c) 12 Image; (d) 25 Image; (e) b2 Image; (f) 4x2Image; (g) 3r2 Image

19. (a) 2 Image; (b) Image Image; (c) 24 Image; (d) 18 Image

20. (a) 24 Image; (b) 54 Image; (c) 150 Image

21. (a) 15; (b) 8; (c) 12; (d) 5

22. (a) 140; (b) 69; (c) 225; (d) 60 Image; (e) 94

23. (a) 150; (b) 204; (c) 39; (d) 64 Image; (e) 160

24. (a) 4; (b) 7; (c) 18 and 9; (d) 9 and 6; (e) 10 and 5

25. (a) 17 and 9; (b) 23 and 13; (c) 17 and 11; (d) 5; (e) 13

26. (a) 36; (b) 38Image; (c) 12 Image; (d) 12x2; (e) 120; (f) 96; (g) 18; (h) Image (i) 32 Image; 98 Image

27. (a) 737; (b) 14; (c) 77

28. (a) 10; (b) 12 and 9; (c) 20 and 10; (d) 5; (e) 2Image

29. 12

34. (a) 1:49; (b) 49:4; (c) 1:3; (d) 1:25; (e) 81: x2; (f) 9:x; (g) 1:2

35. (a) 49:100; (b) 4:9; (c) 25:36; (d) 1:9; (e) 9:4; (f) 1:2

36. (a) 10:1; (b) 1:7; (c) 20:9; (d) 5:11; (e) 2:y; (f) 3x:1; (g) Image:2; (h) 1: 22; (i) x: Image; (j) 2Image:4

37. (a) 6:5; (b) 3:7; (c) Image:1; (d) Image:2; (e) Image:3 or 1:Image

38. (a) 100; (b) 12Image; (c) 12; (d) 100; (e) 105; (f) 18; (g) 20Image

39. (a) 12; (b) 63; (c) 48; (d) 2Image; (e) 45

Chapter 10

1. (a) 200; (b) 24.5; (c) 112; (d) 13; (e) 9; (f) 3Image; (g) 4.5

2. (a) 12Image; (b) 23.47; (c) 7Image; (d) 18.5; (e) 3Image

3. (a) 24°; (b) 24°; (c) 156°

4. (a) 40°; (b) 9; (c) 140°

5. (a) 15°; (b) 15°; (c) 24

6. (a) 5°; (b) 72°; (c) 175°

7. (a) regular octagon; (b) regular hexagon; (c) equilateral triangle; (d) regular decagon; (e) square; (f) regular dodecagon (12 sides)

9. (a) 9; (b) 30; (c) 6 Image; (d) 6; (e) 13Image; (f) 6; (g) 20Image; (h) 60

10. (a) 18 Image; (b) 7 Image; (c) 40; (d) 8 Image; (e) 3.4; (f) 28; (g) 5Image; (h) 2 Image

11. (a) 30 Image; (b) 14; (c) 27; (d) 18; (e) 8Image; (f) 4Image; (g) 48Image; (h) 42; (i) 6; (j) 10; (k) ImageImage; (l) 3Image

12. (a) 817; (b) 3078

13. (a) 54 Image; (b) 96Image; (c) 600Image

14. (a) 576; (b) 324; (c) 100

15. (a) 36Image; (b) 27 Image; (c) ImageImage; (d) 144 3; (e) 3Image; (f) 48Image

16. (a) 10; (b) 10; (c) 5Image

17. (a) 18; (b) 9 Image; (c) 6Image; (d) 3Image”

18. (a) 1:8; (b) 4:9; (c) 9:10; (d) 8:11; (e) 3:1; (f) 2:5; (g) 4 Image:3; (h) 5:2

19. (a) 5:2; (b) 1:5; (c) 1:3; (d) 3:4; (e) 5:1

20. (a) 5:1; (b) 4:7; (c) x:2; (d) Image:1; (e) Image:y; (f) Image:3 Image or Imagex:6

21. (a) 1:4; (b) 1:25; (c) 36:1; (d) 9:100; (e) 49:25

22. (a) 12π; (b) 14π; (c) 10π; (d) 2ππImage

23. (a) 9π; (b) 25π; (c) 64π; (d) Imageπ, (e) 18π

24. (a) C = 10π, A = 25π; (b) r = 8, A = 64π; (c) r = 4, C = 8π

25. (a) 12π; (b) 4π; (c) 7π; (d) 26π; (e) 8Imageπ (f) 3π

26. (a) 98π; (b) I8π; (c) 32π; (d) 25π; (e) 72π; (f) 100π

27. (a) (l) C = 8π, A = 16π; (2) C = 4Imageπ, A= 12π

(b) (l) C = 16π, A = 64π; (2) C = 8Imageπ, A = 48π

(c) (l) C = 12π, A = 36π; (2) C = 6π, A = 9p

(d) (l) C = 16π, A = 64π; (2) C = 8π, A = 16p

(e) (l) C = 20Imageπ, A = 20π; (2) C = 20π A = 100π

(f) (l) C = 6Imageπ, A = 18π; (2) C = 6π, A = 9π

28. (a) 10 ft; (b) 17 ft; (c) 3Image ft or 6.7 ft

29. (a) 2π; (b) 10π; (c) 8; (d) 11π; (e) 6π; (f) 10π

30. (a) 3π; (b) 12Image; (C) 5π; (d) 2π; (e) π; (f) 4π

31. (a) 6π; (b) π/6; (c) 25π/6; (d) 25π; (e) 4Image; (f) 13; (e) 24π; (h) 8π/3

32. (a) 6π; (b) 20; (c) 3π; (d) 16π

33. (a) 120°; (b) 240°; (c) 36°; (d) 180°; (e) 135°; (f) (180/π)° or 57.3° to nearest tenth

34. (a) 72°; (b) 270°; (c) 40°; (d) 150°; (e) 320°

35. (a) 90°; (b) 270°; (c) 45°; (d) 36°

36. (a) 12; (b) 9; (c) 10; (d) 6; (e) 5; (f) 3Image

37. (a) 4; (b) 10; (c) 10 cm; (d) 9

38. (a) 6π–9 Image; (b) 24π–36Image; (c) Image (d) Image (e) Image

39. (a) 4π–8; (b) 150π–225 Image; (c) 24π–36Image; (d) 16π–32; (e) 50π–100

40. (a) Image; (b) 24π–16Image; (c) Image

41. (a) Image (b) Image (c) 4π–8

42. (a) 12π–9 Image; (b) Imageπ (c) 9π–18

43. (a) 200–25π/2; (b) 48 + 26π; (c) 25Image–25π/2; (d) 100π–96; (e) 128–32π; (f) 300π + 400; (g) 39π; (h) 100

44. (a) 36π; (b) 36Image + 18π; (c) 14π

Chapter 11

1. The description of each locus is left for the reader.

Image

2. The diagrams are left for the reader.

(a) The line parallel to the banks and midway between them

(b) The perpendicular bisector of the segment joining the two floats

(c) The bisector of the angle between the roads

(d) The pair of bisectors of the angles between the roads

3. The diagrams are left for the reader.

(a) A circle having the sun as its center and the fixed distance as its radius

(b) A circle concentric to the coast, outside it, and at the fixed distance from it

(c) A pair of parallel lines on either side of the row and 20 ft from it

(d) A circle having the center of the clock as its center and the length of the clock hand as its radius.

4. (a) Image; (b) Image; (c) Image; (d) Image; (e) Image; (f) Image; (g) Image; (h) a 90° are from A to G with B as center

5. (a) Image; (b) Image; (c) Image; (d) Image; (e) E

6. In each case, the letter refers to the circumference of the circle. (a) A; (b) C; (c) B; (d) A; (e) C; (f) A and C; (g) B

7. The description of each locus is left for the reader.

Image

8. (a) images; (b) images (c) line parallel to images and images midway between them; (d) images ; (e) images; (f) images

Image

9. The explanation is left for the reader.

10. (a) The intersection of two of the angle bisectors

(b) The intersection of two of the Image bisectors of the sides

(c) The intersection of the Image bisector of images and the bisector of ∠B

(d) The intersection of the bisector of ∠C and a circle with C as center and 5 as radius

(e) The intersections of two circles, one with B as center and 5 as radius and the other with A as center and 10 as radius

11. (a) 1; (b) 1; (c) 4; (d) 2; (e) 2; (f) 1

Chapter 12

1. A(3, 0); B(4, 3); C(3, 4); D(0, 2); E(–2, 4); F(–4, 2); G(–1, 0); H(–3images,–2); I(–2,–3); J(0,–4); images

3. Perimeter of square formed is 20 units; its area is 25 square units.

4. Area of parallelogram = 30 square units.

Area of ΔBCD = 15 square units.

5. (a) (4, 3); (b) images (c) (–4, 6); (d) (7,–5); (e) images (f) (0, 10); (g) (4,–1); (h) images (i) (5, 5); (j) (–3,–10); (k) (5, 6); (l) (0,–3)

6. (a) (4, 0), (0, 3), (4, 3); (b) (–3, 0), (0, 5), (–3, 5); (c) (6,–2), (0,–2), (6, 0); (d) (4, 6), (4, 9), (3, 8); (e) (2,–3), (–2, 2), (0, 5); (f) images

7. (a) (0, 2), (1, 7), (4, 5), (3, 0); (b) (–2, 7), (3, 6), (6, 1), (1, 2); (c) (–1, 2), (3, 3), (3,–4) (–1,–5); (d) (–2, 1), (4, 2images), (7,–4) (1, 7images)

8. (a) (2, 6), (4, 3); (b) images (c) common midpoint, (2, 2)

9. (a) (–2, 3); (b) (–3,–6); (c) images (d) (a, b); (e) (2a, 3b); (f) (a, b + c)

10. (a) M (4, 8); (b) A (–1, 0); (c) B (6,–3)

11. (a) B images (b) D(3, 3); (c) A(–2, 9)

12. (a) Prove that ABCD is a parallelogram (since opposite sides are congruent) and has a rt. ∠.

(b) The point images is the midpoint of each diagonal.

(c) Yes, since the midpoint of each diagonal is their common point.

13. (a) images (b) E(0, 2), (3, 1); (c) no, since the midpoint of each median is not a common point

14. (a) 5; (b) 6; (c) 10; (d) 12; (e) 5.4; (f) 7.5; (g) 9; (h) a

15. (a) 3, 3, 6; (b) 4, 14, 18; (c) 1, 3, 4; (d) a, 2a, 3a

16. (a) 13; (b) 5; (c) 15; (d) 5; (e) 10; (f) 15; (g) 3 images; (h) 5 images; (i) images; (j) 2 images; (k) 4; (l) a images

18. (a) ΔABC; (b) ΔDEF; (c) ΔGHJ; (d) ΔKLM is not a rt. Δ

19. (a) 5 images; (b) images; (c) images

21. (a) 10; (b) 5; (c) 5images; (d) 13; (e) 4; (f) 3

22. (a) on; (b) on; (c) outside; (d) on; (e) inside; (f) inside; (g) on

23. (a) images (b) images (c) images (d) 3; (e) 2; (f) 1; (g) 5; (h)–2; (i)–3; (j) images (k)–1; (l) 1

24. (a) 3; (b) 4; (c) images (d)–7; (e) 5; (f) 0; (g) 3; (h) 5; (i)–4; (j) images (k)–1; (l)–2; (m) 5; (n) 6; o)–4; (p)–8

25. (a) 72°; (b) 18°; (c) 68°; (d) 22°; (e) 45°; (f) 0°

26. (a) 0.0875; (b) 0.3057; (c) 0.3640; (d) 0.7002; (e) 1; (f) 3.2709; (g) 11.430

27. (a) 0°; (b) 25°; (c) 45°; (d) 55°; (e) 7°; (f) 27°; (g) 37°; (h) 53°; (i) 66°

28. (a) images; images, images, images (b) images, images, images (c) images, images (d) images, images

29. (a) 0; (b) no slope; (c) 5; (d)–5; (e) 0.5; (f)–0.0005

30. (a) 0; (b) no slope; (c) no slope; (d) 0; (e) 5; (f)–1; (g) 2

31. (a) images(b) images; (c)–1; (d) 6

32. (a)–2; (b)–1; (c) images (d) images (e)–10; (f) 1; (g) images; (h) images; (i) no slope; (j) 0

33. (a) 0; (b)–2; (c) 3; (d)–1

34. (a) images (b) images(c) images

35. (a) images(b) 1; (c) 2; (d)–1

36. (a) images (b) images (c) images

37. (a) and (b)

38. (a) 19;(b) 9;(c) 2

39. (a) x =–5; (b) images (c) y = 3 and y =–3; (d) y =–5; (e) x = 4 and x =–4; (f) x = 5 and x =–1; g) y = 4; (h) x = 1; (i) x = 9

40. (a) x = 6; (b) y = 5; (c) x = 6; (d) x = 5; (e) x = 6; (f) y = 3

41. (a) x = y; (b) y = x + 5; (c) x = y–4; (d) y–x = 10; (e) x + y = 12; (f) x–y = 2 or y–x = 2; (g) x = y and x = -y; (h) x + y = 5

42. (a) line having y-intercept 5, slope 2; (b) line passing through (2, 3), slope 4;

(c) line passing through (–2,–3), slope images (d) line passing through origin, slope images

(e) line having y-intercept 7, slope–1; (f) line passing through origin, slope images

43. (a) y = 4x; (b) y =–2x; (c) y = imagesx or 2y = 3x; (d) images (e) y = 0

44. (a) y = 4x + 5; (b) y =–3x + 2; (c) images (d) y = 3x + 8; (e) y =–4x–3; (f) y = 2x or y–2x = 0

45. (a) images (b) images (c) images (d) images

46. (a) y = 4x; (b) images (c) images (d) images (e) y = 2x

47. (a) circle with center at origin and radius 7; (b) x+ + y2 = 16; (c) x2 + y2 = 64 and x2 + y2 = 4

48. (a) x2 + y2 = 25; (b) x2 + y2 = 81; (c) x2 + y2 = 4 or x2 + y2 = 144

49. (a) 3; (b) images(c) 2; (d) images

50. (a) x2 + y2 = 16; (b) x2 + y2 = 121; (c) x2 + y2 = 4 or 9x2 + 9y2 = 4; (d) images or 4x2 + 4y2 = 9; (e) x2 + y2 = 5; (f) images or 4x2 + 4y2 = 3

51. (a) 10; (b) 10; (c) 20; (d) 20; (e) 7; (f) 25

52. (a) 16; (b) 12; (c) 20; (d) 24

53. (a) 10; (b) 12; (c) 22

54. (a) 5; (b) 13; (c) images

55. (a) 6; (b) 10; (c) 1.2

56. (a) 15; (b) 49; (c) 53

57. (a) 30; (b) 49; (c) 88; (d) 24; (e) 16; (f) 18

Chapter 13

1. (a) <; (b) >; (c) >; (d) >; (e) >; (f) <

2. (a) >; (b) >; (c) <; (d) >

3. (a) >; (b) <; (c) <; (d) >

4. (a) more; (b) less

5. (a) >; (b) >; (c) <; (d) > (e) <; (f) <;

6. (c), (d), and (e)

7. (a) 5 to 7; (b) 6 to 10; (c) 4 to 10; (d) 3 to 9; (e) 2 to 8; (f) 1 to 13

8. (a)∠B,∠A,∠C; (b) images, images,images; (c) ∠3, ∠2, ∠1

9. (a) m∠BAC > m∠ACD; (b) AB > BC

10. (a) images,images,images (b) ∠BOC ∠AOB ∠AOC (c) images,images ≐ images,images (d) images,images,images

Chapter 14

1. (a) Ornament, jewelry, ring, wedding ring; (b) vehicle, automobile, commercial automobile, taxi; (c) polygon, quadrilateral, parallelogram, rhombus; (d) angle, obtuse angle, obtuse triangle, isosceles obtuse triangle

2. (a) A regular polygon is an equilateral and an equiangular polygon.

(b) An isosceles triangle is a triangle having at least two congruent sides.

(c) A pentagon is a polygon having five sides.

(d) A rectangle is a parallelogram having one right angle.

(e) An inscribed angle is an angle formed by two chords and having its vertex on the circumference of the circle.

(f) A parallelogram is a quadrilateral whose opposite sides are parallel.

(g) An obtuse angle is an angle larger than a right angle and less than a straight angle.

3. (a) x + 2 ≠ 4; (b) 3y = 15; (c) she does not love you; (d) his mark was not more than 65; (e) Joe is not heavier than Dick; (f) a + b = c

4. (a) A nonsquare does not have congruent diagonals. False (for example, when applied to a rectangle or a regular pentagon).

(b) A non-equiangular triangle is not equilateral. True.

(c) A person who is not a bachelor is a married person. This inverse is false when applied to an unmarried female.

(d) A number that is not zero is a positive number. This inverse is false when applied to negative numbers.

5. (a) Converse true, inverse true, contrapositive true

(b) Converse false, inverse false, contrapositive true

(c) Converse true, inverse true, contrapositive true

(d) Converse false, inverse false, contrapositive true

6. (a) Partial converses: interchange (2) and (3) or (1) and (3) Partial inverses: negate (1) and (3) or (2) and (3)

(b) Partial converses: interchange (1) and (4) or (2) and (4) or (3) and (4) Partial inverses: negate (1) and (4) or (2) and (4) or (3) and (4)

7. (a) Necessary and sufficient; (b) necessary but not sufficient; (c) neither necessary nor sufficient; (d) sufficient but not necessary; (e) necessary and sufficient; (f) sufficient but not necessary; (g) necessary but not sufficient

Chapter 17

1. (a) 6(72) or 294 yd2; (b) 2(8)(6 Image) + 2(8)(14) + 2(6Image)(14) or 510 ft2; (c) 4(3.14)302 or 11,304 m2; (d) (3.14)(10)(10 + 41Image or 911 yd2

2. (a) 363 or 46,656 in3; (b) 1003 or 1,000,000 cm3

3. (a) 27 in3; (b) 91 in3; (c) 422 in3; (d) 47 in3; (e) 2744 in3

4. (a) 3(8Image)(8) or 204 in3; (b) 2(9)(9) or 162 ft3; (c) Image or 13 6)(6.4) ft3

5. (a) 904 m3; (b) 1130 ft3; (c) 18 ft3

6. (a) V = Image π r2 (b) V = Images2h; (c) V = Imagelwh; (d) V = Image π r3

7. (a) Image (b) Image (c) 3πr3

Chapter 18

1. (a) A′ (9, 2), B′ (2, 4), and C′(5, 7); (b) A′ (–4, 2), B′ (3, 4), and C′ (0, 7); (c) A′ (–5, 1), B′ (2,–1), and C′ (–1,–4); (d) A′ (–2, 14), B′ (–4, 7), and C′ (–7, 10); (e) A′ (12, 4), B′ (–2, 8), and C′ (4, 14); (f) A′ (–14, 6), B′ (7, 12), and C′ (–2, 21); (g) A′ (0,–1), B′ (–2, 6), and C′ (–5, 3)

2. (a) A′ (6,–1), B′ (7, 2), and C′ (8,–1); (b) A′ (1,–5), B′ (2,–2), and C′ (3,–5); (c) A′ (–2, 1), B′ (–1, 4), and C′ (0, 1)

3. (a) translation to the right 5 spaces, P(x, y) Image P′(x + 5, y); (b) translation down 5 spaces and to the right 3, P(x, y) Image P′(x + 3, y–5); (c) translation down 3 spaces and to the left 5, P(x, y) Image P′(x–5, y–3)

4. (a) P(x, y) Image P′(x, y–5); (b) P(x, y) Image P′(x + 6, y); (c) P(x, y) Image P′(x–7, y + 3); (d) P(x, y) Image P′(x + 8, y–2); (e) P(x, y) Image P′(x–1, y + 4)

5. (a) A′(–1, 3), B′(–5, 3), C′(–4, 1), and D′(–2, 1); (b) A0(1,–5), B′(5,–5), C″′(4,–3), and D″(2,–3); (c) A-(15, 3), B-(11, 3), C-(12, 1), and D′″(14, 1)

6. (a) reflection across the line x = 2, P(x, y) Image P′(4–x, y); (b) reflection across y = 3, P(x, y) Image P′(x, 6–y); (c) reflection across x–5, P(x, y) A P′″(–10–x, y)

7. (a) P(x, y) Image P′(x, 10–y); (b) P(x, y) Image P′(–4–x, y); (c) P(x, y) Image P′(x,–2–y); (d) P(x, y) Image P′(5–x, y)

8. (a), (b), (e), and (f)

9. (a) A′(2,–1), B′(2,–4), C′(1,–5), and D′(1,–2); (b) A0(–1,–2), B0(–4,–2), C0(–5,–1), and D″(–2,–1); (c) A″′(–2, 1), B″′(–2, 4), C-(–1, 5), and D-(–1, 2)

10. (a) 180° rotation about the origin, P(x, y) Image P′(–x,–y); (b) 90° clockwise rotation about the origin, P(x, y) Image P′(y,–x); (c) 270° clockwise rotation about the origin (or 90° counter-clockwise), P(x, y) A P″(–x, y)

11. (a) P(x, y) Image P′(x cos 40° + y sin 40°, y cos 40°–x sin 40°) = P′(0.766x + 0.6428y, 0.766y–0.6428x); (b) P(x, y) Image P′(x cos 50° + y sin 50°, y cos 50°–x sin 50°) = P′(0.6428x + 0.766y, 0.6428y–0.766x); (c) P(x, y) Image P′(x cos 80° + y sin 80°, y cos 80°–x sin 80°) = P′(0.1736x + 0.9848y, 0.1736y–0.9848x)

12. (a) 120°; (b) 60°; (c) 72°; (d) 360° (no rotational symmetry); (e) 90°; (f) 180°

13. (a) A′(4, 5), B′(5, 4), and C′(5, 7); (b) A′(2,–5), B″(3,–6), and C0(0,–6); (c) A″′(–1,–2), B″′(–2,–3), and C″′(1,–3); (d) A″′(–4, 3), B(–5, 4), and C″(–5, 1)

14. (a) R(x, y) Image R′(x + 6, y–1); (b) R(x, y) Image R′(1–x, y + 2); (c) R(x, y) Image R′(y + 3,–x–6); (d) R(x, y) Image R′(–y, 4–x); (e) R(x, y) Image R′(6–x,–3–y)

15. (a) reflect across the y axis and then move down 2 and to the right 3 spaces, P(x, y) Image P′(–x + 3, y–2); (b) rotate about the origin counterclockwise 90°, then move to the left 1 space, P(x, y) Image P′(–y–1, x); (c) rotate around the origin 90° clockwise, then reflect across the x axis, then move down and to the right 1 space, P(x, y) A P″(y + 1, x–1)

16. (a) P(x, y) Image P′(x,–y–3); (b) P(x, y) Image P′(y + 2,–x); (c) P(x, y) Image P′(–x, y–4); (d) P(x, y) Image P′(–x, 4 + y); (e) P(x, y) Image P′(–7–x, y + 3)

17. A′(–3, 6), B′(3, 6), C′(3, 3), and D′(–3, 3)

18. (a) P(x, y) Image P′(2x, 2y); (b) P(x, y) Image P′(8x, 8y); (c) P(x, y) Image P′(Imagex, Imagex