Example 4.1 from Elementary Algebra, 4.1 Use the Rectangular Coordinate System

Use the Rectangular Coordinate System: example 4.1

Plot each point in the rectangular coordinate system and identify the quadrant in which the point is located:

ⓐ $(−5, 4)$ ⓑ $(−3, −4)$ ⓒ $(2, −3)$ ⓓ $(−2, 3)$ ⓔ $(3, \frac{5}{2})$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
The first number of the coordinate pair is the x-coordinate, and the second number is the y-coordinate.
1. ⓐ Since $x = −5$ , the point is to the left of the y-axis. Also, since $y = 4$ , the point is above the x-axis. The point $(−5, 4)$ is in Quadrant II.
2. ⓑ Since $x = −3$ , the point is to the left of the y-axis. Also, since $y = −4$ , the point is below the x-axis. The point $(−3, −4)$ is in Quadrant III.
3. ⓒ Since $x = 2$ , the point is to the right of the y-axis. Since $y = −3$ , the point is below the x-axis. The point $(2, −3)$ is in Quadrant lV.
4. ⓓ Since $x = −2$ , the point is to the left of the y-axis. Since $y = 3$ , the point is above the x-axis. The point $(−2, 3)$ is in Quadrant II.
5. ⓔ Since $x = 3$ , the point is to the right of the y-axis. Since $(4, −4)$ , the point is above the x-axis. (It may be helpful to write $\frac{5}{2}$ as a mixed number or decimal.) The point $(3, \frac{5}{2})$ is in Quadrant I.
  
  Figure 4.3

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Plot each point in a rectangular coordinate system and identify the quadrant in which the point is located:

ⓐ $(−2, 1)$ ⓑ $(−3, −1)$ ⓒ $(4, −4)$ ⓓ $(−4, 4)$ ⓔ $(−4, \frac{3}{2})$ .

How did it go?