Coordinate Plane — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. A path goes from (0, 0) to (4, 0) to (4, 3) to (0, 3) and back to (0, 0). What is the total distance?
A) 12 units
B) 14 units
C) 10 units
D) 16 units
Add each segment: 4 units right + 3 units up + 4 units left + 3 units down = 14 units total around the rectangle.
2. Three corners of a square are at (2, 1), (6, 1), and (6, 5). Where is the fourth corner?
A) (2, 5)
B) (1, 5)
C) (5, 2)
D) (2, 6)
The missing corner must share x = 2 with (2, 1) and y = 5 with (6, 5), forming the point (2, 5) to complete the square.
3. Point M is at (1, 4). It moves 5 units right, then 2 units down, then 3 units left. Where is it now?
A) (4, 2)
B) (3, 2)
C) (3, 6)
D) (2, 3)
Track each move: x goes 1 + 5 = 6, then y goes 4 - 2 = 2, then x goes 6 - 3 = 3. The final position is (3, 2).
4. Which pair of points has a distance of exactly 9 units?
A) (0, 1) and (9, 1)
B) (2, 3) and (2, 10)
C) (1, 0) and (1, 8)
D) (3, 5) and (3, 12)
Both points share y = 1, so the distance is the difference in x-values: 9 - 0 = 9 units apart.
Part B: Fill in the Blank
Write the correct answer on each line.
1. A triangle has vertices at (1, 1), (1, 6), and (7, 1). The height is 5 units.
The height runs vertically from (1, 1) to (1, 6), so subtract the y-values: 6 - 1 = 5 units.
2. Using the same triangle, the base is 6 units.
The base runs horizontally from (1, 1) to (7, 1), so subtract the x-values: 7 - 1 = 6 units.
3. A point at (2, 5) moves 4 right and 3 down. Its new coordinates are (6, 2).
Add 4 to the x-coordinate: 2 + 4 = 6. Subtract 3 from the y-coordinate: 5 - 3 = 2. The new position is (6, 2).
4. Two points share the same x-coordinate of 4. One is at (4, 2) and the other at (4, 10). They are 8 units apart.
Since both points share x = 4, they are on the same vertical line. Subtract the y-values: 10 - 2 = 8 units apart.
5. A rectangle has an area of 30 square units. One pair of sides runs from x = 1 to x = 6. The height is 6 units.
The base is 6 - 1 = 5 units. Since area = base x height, divide 30 ÷ 5 = 6 units for the height.