Coordinate Plane — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. A rectangle has three corners at (1, 2), (1, 7), and (6, 7). Where is the fourth corner?
A) (6, 2)
B) (7, 6)
C) (2, 6)
D) (6, 1)
The rectangle needs a fourth corner at x=6 (matching the third corner) and y=2 (matching the first corner). The missing corner is (6, 2).
2. Points A(2,3), B(2,6), and C(5,6) form a right triangle. What is the total distance from A to B to C?
A) 6 units
B) 8 units
C) 5 units
D) 9 units
A to B: same x, distance = |6−3| = 3 units. B to C: same y, distance = |5−2| = 3 units. Total = 3 + 3 = 6 units.
3. A point starts at (1, 1), moves 3 units right, then 4 units up, then 2 units right. What are the final coordinates?
A) (5, 6)
B) (6, 5)
C) (3, 4)
D) (4, 7)
Start (1,1). Move 3 right: (4,1). Move 4 up: (4,5). Move 2 right: (6,5). Final coordinates: (6, 5).
4. Which pair of points is exactly 7 units apart?
A) (1, 2) and (1, 9)
B) (0, 3) and (6, 3)
C) (2, 2) and (2, 8)
D) (3, 0) and (3, 5)
(1,2) and (1,9): same x, distance = |9−2| = 7 units. The other pairs: 6 units, 6 units, and 5 units apart.
Part B: Fill in the Blank
Write the correct answer on each line.
1. A square has corners at (2, 3) and (2, 8). The side length is 5 units.
The two given corners are on the same vertical side. Side length = |8 − 3| = 5 units.
2. A point at (4, 1) moves 3 units right and 5 units up. Its new position is (7, 6).
Move 3 right: x = 4 + 3 = 7. Move 5 up: y = 1 + 5 = 6. New position: (7, 6).
3. The perimeter of a rectangle with corners at (0, 0), (5, 0), (5, 3), and (0, 3) is 16 units.
Width = |5 − 0| = 5 units. Height = |3 − 0| = 3 units. Perimeter = 2 × (5 + 3) = 16 units.
4. Two points are 6 units apart horizontally. One is at (1, 4). The other is at (7, 4).
Moving 6 units right from x=1: 1 + 6 = 7. The other point is at (7, 4).
5. A triangle has vertices at (0, 0), (8, 0), and (4, 6). The length of the base is 8 units.
The base connects (0,0) and (8,0), both on y=0. Base length = |8 − 0| = 8 units.