Knowing Ranges

Now try having even less information. Instead of knowing the actual x-coordinate, see what happens if all you know is a range of possible values for x. What do you do if all you know is that x > 0? To answer that, return to the number line for a moment. As you saw earlier, if x > 0, then the target is anywhere to the right of 0:

Now look at the coordinate plane. All you know is that x is greater than 0. And you don’t know anything about y, which could be any number.

How do you show all the possible points? You can shade in part of the coordinate plane: the part to the right of 0.

If you know that x > 0…

Then you know...

 Every point in the shaded region has an x-coordinate greater than 0.

Now say that all you know is y < 0. Then you can shade in the bottom half of the coordinate plane (see figure that follows)—where the y-coordinate is less than 0. The x-coordinate can be anything. Notice that the dashed line in the plane indicates that y cannot be 0. It must be below the dashed line.

If you know that y < 0…

Then you know...

 Every point in the shaded region has a y-coordinate less than 0.

Finally, if you know information about both x and y, then you can narrow down the shaded region.

If you know that x > 0 AND y < 0…

Then you know...

The only place where x is greater than 0 AND y is less than 0 is the bottom right quarter of the plane. So you know that the point lies somewhere in the bottom right quarter of the coordinate plane.

The four quarters of the coordinate plane are called quadrants. Each quadrant corresponds to a different combination of signs of x and y. The quadrants are always numbered as shown here, starting on the top right and going counter-clockwise:

Check Your Skills

  1. In which quadrant do each of the following points lie?

    1. (1, −2)
    2. (−4.6, 7)
    3. (−1, −2.5)
    4. (3, 3)

  2. Which quadrant or quadrants are indicated by the following?

    1. x < 0, y > 0
    2. x < 0, y < 0
    3. y > 0
    4. x < 0