﻿ Coordinate Plane Worksheet | Problems & Solutions Coordinate Plane Worksheet

Coordinate Plane Worksheet
• Page 1
1.
If the distance between P(20, $a$) and Q (8, - 8) is 20 units, then what is the value of $a$? a. - 8 and 24 b. 16 c. 15.32 and 31.32 d. 8 and - 24

Solution:

The distance between two points A(x1, y1) and B(x2, y2) is (x2-x1)²+(y2-y1)²
[The Distance Formula.]

PQ = (20 - 8)2+(a - (- 8))2 = 20
[From step 1.]

122+(a +8)2 = 20
[Simplify.]

144 + (a + 8)2 = 202 = 400
[Squaring on both sides.]

(a + 8)2 = 400 - 144 = 256
[Rearrange.]

a + 8 = 256 = ± 16
[Take square roots on both sides.]

a = ± 16 - 8
[Solve for a.]

a = - 24 or a = + 8

2.
Find the coordinates of the points that lie on the graph $y$ = 3$x$ - 2. a. (- 2, - 4) b. (- 1, 1) c. (3, 5) d. (2, 4)

Solution:

The equation of the line is y = 3x - 2.
[Given.]

Substitute the points in the equation and verify.

For coordinates (- 1, 1), 1 = 3(- 1) - 2
1 ≠ - 5

For coordinates (- 2, - 4), - 4 = 3(- 2) - 2
- 4 ≠ - 8

For coordinates (3, 5), 5 = 3(3) - 2
5 ≠ 7

For coordinates (2, 4), 4 = 3(2) - 2
4 = 4

So, the point (2, 4) lie on the line y = 3x - 2

3.
Find the coordinates of the point that doesnot lie on the 2$x$ = - $y$ + 3. a. (2, -2) b. (- 1, 5) c. (1, - 1) d. (- 3, 9)

Solution:

The equation of the line is 2x = - y + 3.
[Given.]

Substitute the points in the equation and verify.

For coordinates (1, - 1), 2(1) = - 1 + 3
2 = 2

For coordinates (- 3, 9), 2(- 3) = - 9 + 3
- 6 = - 6

For coordinates (- 1, 5), 2(- 1) = - 5 + 3
- 2 = - 2

For coordinates (2, - 2), 2(2) = - (2) + 3
4 ≠ 1

So, the point (2, - 2) does not lie on the line 2x = - y + 3

4.
Plot the points (2, 1),(4, 1) and (4, 4) and join them. What do you notice? a. A triangle is formed b. A rectangle is formed c. A square is formed d. None of the above

5.
Identify the ordered pair that corresponds to the point B.  a. (2, 2) b. (- 2, 2) c. (2, - 2) d. (- 2, - 2)

6.
Find the coordinates of the apple placed on the coordinate plane.  a. (4, 1) b. (0, 4) c. (1, 4) d. (4, 0)

7.
Find the coordinates of point X on the scatter plot.  a. (6, 3) b. (4, 2) c. (5, 3) d. (4, 7)

8.
Name the point having the coordinates (- 2.5, 2.5) on the coordinate plane.  a. C b. E c. B d. G

9.
Graph the point A (- 4, 3) on a coordinate plane.  a. Graph 1 b. Graph 2 c. Graph 3 d. Graph 4  a. Plot 1 b. Plot 2 c. Plot 3 d. Plot 4