Coordinate Geometry Worksheet - Page 3

Coordinate Geometry Worksheet
• Page 3
21.
Find the slope of the line joining the midpoints of the sides $\stackrel{‾}{\mathrm{AB}}$ and $\stackrel{‾}{\mathrm{CD}}$ of the quadrilateral represented by A(10, 10), B(6, 4), C(18, 12) and D(10, 16).
 a. $\frac{8}{7}$ b. $\frac{4}{3}$ c. $\frac{7}{6}$ d. 1

Solution:

Midpoint of AB = (10+62, 10+42) = (8, 7)

Midpoint of CD = (18+102, 12+162) = (14, 14)

Slope of the line joining the midpoints = 14-714-8 = 76 = 7 / 6

22.
Which has a longer diagonal?
A rectangle ABCD represented by A(0, 0), B(9 , 0), C(9, 12) and D(0, 12) or Square PQRS having P(2, 6) and Q(11, 18).
 a. Rectangle b. Square

Solution:

Length of diagonal of ABCD = AC = BD = 92+122 = 15
[Distance formula.]

Length of diagonal of PQRS = PR = QS = 2.(2 - 11)2+(6 - 18)2
[Length of the diagonal of a square = a2, where a is the length of the side of a square.]

= 2.(-9)2 +(-12)2 =2.81+144 = 152

Square has the longer diagonal.

23.
A parallelogram is represented by P(2, 6), Q(14, 6), R(20, 8) and S(8, 8). If the origin is shifted to the point of intersection of it's diagonals, then what would be the coordinates of P?

 a. (- 9, - 1) b. (- 2 , - 6) c. (9, 1) d. (13, 13)

Solution:

Point of intersection of the diagonals = Midpoint of the diagonals = (2 + 202, 6 + 82) = (11, 7)

New x-coordinate of P = 2 - 11 = - 9
[Present x-coordinate of P - present x-coordinate of the midpoint of the diagonals.]

New y-coordinate of P = 6 - 7 = - 1
[Present y-coordinate of P - present y-coordinate of the midpoint of the diagonals.]

The coordinates of the P after shifing the point P is (- 9, - 1)

24.
How will Jesse go from the Gymnasium to the Basketball Court?

 a. 3 units to the right and then 2 units down b. 5 units to the left and then 3 units up c. 3 units to the left and then 2 units up d. 5 units to the right and then 3 units down

Solution:

From the Gymnasium, Jesse should move 3 units to the left and then 2 units up to reach the Basketball Court.

25.
Sasha is at the school. How will she go to her house?

 a. 5 units to the right and then 4 units up b. 4 units to the right and then 5 units up c. 5 units to the right and then 5 units up d. 4 units to the right and then 4 units up

Solution:

Sasha has to move 5 units to the right and 5 units up to reach her house.

26.
Danny moved 4 units to the right and 2 units down from his house. Where did he go?

 a. Playground b. Chapel c. Cafeteria d. Outlet

Solution:

If Danny moves 4 units to the right and 2 units down from his House, he will go to the Cafeteria.

27.
Michael was at the playground. He moved 4 units to the right and 1 unit down. Where did he go?

 a. Complex b. Recreation Hall c. Visitors Parking d. Childcare Center

Solution:

If Michael moves 4 units to the left and 1 unit down from the Playground, he reaches the Childcare Center.

So, Michael went to the Childcare Center.

28.
From point D, if Jane moves 4 units up, 5 units to the right, and then 6 units down,where will she reach?

 a. I b. K c. M d. L

Solution:

From point D, if Jane moves 4 units up, 5 units to the right and 6 units down, she will reach the point L.

29.
Which ordered pair tells you the location of the kids park?

 a. (4, 6) b. (6, 5) c. (6, 4) d. (5, 6)

Solution:

Kids park is 5 spaces to the right of zero and 6 spaces up of zero.

So, the kids park is located at the point (5, 6).

30.
At what point is the watch store?

 a. (1, 0) b. (1, 1) c. (0, 1) d. (1, 2)

Solution:

The watch store is 0 spaces to the right of zero and 1 space up of zero.

So, the watch store is located at the point (0, 1).