# Coordinate Geometry Worksheet - Page 6

Coordinate Geometry Worksheet
• Page 6
51.
Find the location of the vertex D, if ABCD forms a square.

 a. (6, 6) b. (6, 3) c. (3, 3) d. (3, 6)

#### Solution:

From the graph, the vertex A is (3, 3), the vertex B is (6, 3), and the vertex C is (6, 6).

If ABCD forms a square, then the x-coordinate of the vertex D should be equal to the x-coordinate of the vertex A and the y-coordinate of the vertex D should be equal to the y-coordinate of the vertex C and it looks like below.

From the above graph, the vertex D is (3, 6).

So, the location of the other vertex D is (3, 6).

52.
Find the location of the vertex R, if PQRS forms a rectangle.

 a. (6, 8) b. (6, 2) c. (2, 6) d. (8, 6)

#### Solution:

From the graph, the vertex P is (2, 2), the vertex Q is (2, 8), and the vertex S is (6, 2).

If PQRS forms a rectangle, then the x-coordinate of the vertex R should be equal to the x-coordinate of the vertex S and the y-coordinate of the vertex R should be equal to the y-coordinate of the vertex Q.

From the above graph, the vertex R is (6, 8).

So, the location of the vertex R is (6, 8).

53.
Which is the location of the vertex N, if KLMN is a square?

 a. (- 9, 9) b. (9, - 9) c. (8, 9) d. (9, 9)

#### Solution:

From the graph, the vertex K is (6, 9), the vertex L is (6, 6), and the vertex M is (9, 6).

If KLMN forms a square, then the x-coordinate of the vertex N should be equal to the x-coordinate of the vertex M and the y-coordinate of the vertex N should be equal to the y-coordinate of the vertex K and it looks like below.

From the above graph, the vertex N is (9, 9).

So, the location of the vertex N is (9, 9).

54.
Identify the relationship between the coordinates of the vertices P and Q.

 a. P and Q have same $y$-coordinate b. $y$-coordinate of P is 2 units less than $y$-coordinate of Q. c. $x$-coordinate of P is 2 units more than $x$-coordinate of Q. d. P and Q have same $x$-coordinate

#### Solution:

From the graph, the ordered pairs of P and Q are (3, 3) and (5, 3).

As the second number in the ordered pairs of P and Q are same, there is no change in their y-coordinates.

The relationship between the coordinates of the vertices P and Q is, both have same y-coordinate.

55.
Identify the relationship between the coordinates of the vertices C and D.

 a. Both have same $x$-coordinate b. $x$-coordinate of C is 4 more than $x$-coordinate of D c. $y$-coordinate of C is 4 less than $y$-coordinate of D d. Both have same $y$-coordinate

#### Solution:

From the graph, the ordered pairs of C and D are (7, 6) and (7, 2).

As the first number in the ordered pairs of C and D are same, there is no change in their x-coordinates.

The relationship between the coordinates of the vertices C and D is, both have same x-coordinate.

56.
How far is the Cafeteria from the Lake?

 a. 4 units b. 5 units c. 3 units d. 6 units

#### Solution:

The line joining the Lake and the Cafeteria is a vertical line segment.

The length of a vertical line segment on a coordinate plane equals the difference between the y-coordinates.

The Cafeteria is located on the ordered pair (4, 2) and the Lake is on the ordered pair (4, 7).

So, the distance between the Cafeteria from the Lake = 7 - 2 = 5.
[Difference between the y-coordinates.]

The Cafeteria is 5 units far from the Lake.

57.
Find the distance between the Playground and the Tenniscourt.

 a. 5 units b. 3 units c. 4 units d. 2 units

58.
Find the length of the line segments joining the points A(7, 4) and B(9, 4).
 a. 20 units b. 16 units c. 9 units d. 2 units

59.
Find the length of the line segments joining the points A(9, 2) and B(13, 2).
 a. 4 units b. 24 units c. 22 units d. 13 units