Grade 7 Coordinates & Transformations worksheet
from Gradelings · Name: ______________________
How to explain it
- A point is (x, y). Go across for x, then up or down for y.
- A translation adds or subtracts from x and y.
- A reflection in the x-axis changes the sign of y.
Example: Move the point (2, 3) right 4 and down 1. Where does it land? Right 4: x = 2 + 4 = 6. Down 1: y = 3 − 1 = 2. Answer: (6, 2)
Question 1
How many units apart are A(-3, 5) and B(4, 5)?
answer boxunits
7 units
Hint: They have the same y-coordinate, so count across: 4 − (-3) = 7 units.
Question 2
Where is the point (1, -13)?
- Quadrant I
- Quadrant III
- Quadrant IV
- Quadrant II
Quadrant IV
Hint: Quadrant I is (+, +), II is (−, +), III is (−, −) and IV is (+, −), going counterclockwise from the top right. A point with a 0 coordinate sits on an axis.
Question 3
What are the coordinates of point A?
- (-5, 3)
- (3, 5)
- (5, 3)
- (5, -3)
(5, 3)
Hint: Start at the origin (0, 0). Move 5 right along the x-axis, so x = 5. Then move 3 up, so y = 3. Write x first: (5, 3).
Question 4
Which single transformation moves point A to A′?
- Reflection in the y-axis
- Translation 4 units right
- Rotation of 180° about the origin
- Reflection in the x-axis
Rotation of 180° about the origin
Hint: Both coordinates changed sign: (3, 4) → (-3, -4). That's a rotation of 180° about the origin.
Question 5
Point P(3, 2) is rotated 180° about the origin. What are the coordinates of its image, P′?
- (3, -2)
- (-3, -2)
- (2, 3)
- (-3, 2)
(-3, -2)
Hint: A 180° rotation about the origin changes the sign of both coordinates: (3, 2) → (-3, -2).
Question 6
Rectangle ABCD has vertices A(-2, 3), B(5, 3), C(5, -3) and D(-2, -3). What is its area?
answer boxsq. units
42 sq. units
Hint: Width: 5 − (-2) = 7. Height: 3 − (-3) = 6. Area = 7 × 6 = 42 square units.
Question 7
Point P(-3, -1) is translated 3 units left and 4 units up. What are the coordinates of its image, P′?
- (-6, -5)
- (-6, 3)
- (1, -4)
- (0, -5)
(-6, 3)
Hint: Right adds to x and left subtracts from x. Up adds to y and down subtracts from y. So P′ = (-6, 3).
Question 8
Point A(1, -2) is translated 5 units right and 4 units up. What is the x-coordinate of its image, A′?
answer box
6
Hint: x: 1 + 5 = 6. y: -2 + 4 = 2.
Question 9
Point A(4, -3) is translated 2 units up. What is the y-coordinate of its image, A′?
answer box
-1
Hint: Moving up adds to y: -3 + 2 = -1.
Question 10
Rectangle ABCD has vertices A(-1, 2), B(3, 2), C(3, -3) and D(-1, -3). What is its perimeter?
answer boxunits
18 units
Hint: Width: 3 − (-1) = 4. Height: 2 − (-3) = 5. Perimeter = 2 × (4 + 5) = 18 units.
Answer key
- 1. 7 units
- 2. Quadrant IV
- 3. (5, 3)
- 4. Rotation of 180° about the origin
- 5. (-3, -2)
- 6. 42 sq. units
- 7. (-6, 3)
- 8. 6
- 9. -1
- 10. 18 units
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