Grade 6 Transformations worksheet
from Gradelings · Name: ______________________
How to explain it
- A translation slides a shape without turning it.
- A reflection flips a shape over a line.
- A rotation turns a shape around a point.
Example: A shape moves 3 squares to the right and does not turn or flip. Which transformation is it? It only slides. A slide is a translation. Answer: A translation
Question 1
Triangle ABC is translated 3 units right and 1 unit up. What is the x-coordinate of B′?
answer box
7
Hint: Read B's x-coordinate. Moving right adds to x; moving left subtracts. Up and down don't change x.
Question 2
Reflect point P in the vertical mirror line x = 6 (the dotted line). Where is its image, P′?
- (8, 5)
- (5, 8)
- (6, 8)
- (7, 4)
(5, 8)
Hint: Count how far P is from the mirror line. The image is the same distance on the other side. In a vertical mirror line, the y-coordinate stays the same.
Question 3
Point Q is reflected in the horizontal mirror line y = 5 (the dotted line). What is the y-coordinate of Q′?
answer box
10
Hint: Count how far Q is below the line. Q′ is the same distance on the other side. The x-coordinate doesn't change.
Question 4
A shape is translated, then reflected, then rotated. How does the final image compare with the original?
- Half the size
- Same size but a different shape
- Twice as big
- Same size and shape (congruent)
Same size and shape (congruent)
Hint: Slides, flips and turns move a shape around, but they never stretch or shrink it.
Question 5
Rotate point P 90° clockwise around the centre C(5, 5). Where does P land?
- (4, 9)
- (4, 1)
- (1, 4)
- (6, 9)
(4, 1)
Hint: Picture a line from C to P and turn it a quarter turn clockwise. Clockwise, a point above C moves to the right of C, and a point right of C moves below it.
Question 6
What are the coordinates of point A?
- (8, 8)
- (9, 8)
- (10, 7)
- (8, 9)
(9, 8)
Hint: Start at (0, 0). Go across to find x first, then up to find y. Write them as (x, y).
Question 7
Point P(2, 7) is translated 1 unit left and 1 unit up, then reflected in the mirror line x = 5. Where does it end up?
- (9, 8)
- (1, 8)
- (8, 7)
- (9, 7)
(9, 8)
Hint: Do one step at a time. After the translation P is at (1, 8). Then reflect: the y-coordinate stays the same, and the new x is the same distance on the other side of x = 5.
Question 8
Point P is translated 5 units right and 1 unit down. Where is its image, P′?
- (9, 3)
- (2, 9)
- (8, 3)
- (8, 5)
(8, 3)
Hint: Move across first: right adds to x and left subtracts. Then move up (add to y) or down (subtract from y).
Question 9
Point P is translated 2 units right and 3 units up. Where is its image, P′?
- (3, 4)
- (8, 10)
- (7, 10)
- (8, 9)
(7, 10)
Hint: Move across first: right adds to x and left subtracts. Then move up (add to y) or down (subtract from y).
Question 10
Triangle ABC is translated 3 units left and 2 units up. What is the x-coordinate of B′?
answer box
3
Hint: Read B's x-coordinate. Moving right adds to x; moving left subtracts. Up and down don't change x.
Answer key
- 1. 7
- 2. (5, 8)
- 3. 10
- 4. Same size and shape (congruent)
- 5. (4, 1)
- 6. (9, 8)
- 7. (9, 8)
- 8. (8, 3)
- 9. (7, 10)
- 10. 3
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