Transformations: translations, reflections & rotations

A transformation changes the position, orientation or size of a shape. A translation slides a shape without turning or flipping it — every point moves the same distance in the same direction. A reflection flips a shape over a line (called the axis of reflection), creating a mirror image. A rotation turns a shape around a fixed point by a certain angle, like 90° or 180°. In all three, the shape's size and angles stay exactly the same — only its position or orientation changes.

Key terms

Translation:

Sliding a shape without turning or flipping it.

Reflection:

Flipping a shape over a line to create a mirror image.

Rotation:

Turning a shape around a fixed point by an angle.

Questions

1. 1. A translation:

   • Flips a shape
   • Slides a shape
   • Turns a shape
   • Resizes a shape

2. 2. A reflection:

   • Slides a shape
   • Flips a shape to create a mirror image
   • Turns a shape
   • Resizes a shape

3. 3. A rotation:

   • Slides a shape
   • Flips a shape
   • Turns a shape around a point
   • Resizes a shape

4. 4. In a translation, every point moves:

   • Randomly
   • The same distance in the same direction
   • In a circle
   • Not at all

5. 5. A reflection creates a:

   • Bigger shape
   • Smaller shape
   • Mirror image
   • Random shape

6. 6. Do transformations change a shape's size?

   • Yes, always
   • No, they only change position or orientation
   • Only rotations do
   • Only reflections do

7. 7. Looking in a mirror is an example of a:

   • Translation
   • Reflection
   • Rotation
   • Resize

8. 8. A shape rotated 180° ends up:

   • In the exact same position
   • Facing the opposite direction
   • Twice as big
   • Half the size

9. 9. A shape translated 5 units right and 3 units up moves:

   • Only right
   • Only up
   • Right and up
   • Left and down

10. 10. A shape reflected over a vertical line will:

    • Stay in the same place
    • Flip left-right
    • Flip up-down
    • Rotate 90°

11. 11. A shape rotated 90° clockwise around a point:

    • Doesn't move
    • Turns a quarter turn
    • Turns a half turn
    • Turns a full turn

12. 12. Which transformation would you use to slide a shape 4 units to the left?

    • Reflection
    • Rotation
    • Translation
    • Resize

13. 13. After a rotation, a shape's angles:

    • Change
    • Stay the same
    • Double
    • Disappear

14. 14. A shape and its reflection are:

    • Identical in every way including position
    • The same size and shape but mirrored
    • Different sizes
    • Unrelated shapes

15. 15. A triangle is rotated 360° around a point. Where does it end up?

    • Upside down
    • Back in its original position
    • Twice as big
    • Mirrored

16. 16. A shape is translated, then reflected. Compared to the original, the final shape's size is:

    • Bigger
    • Smaller
    • The same
    • Impossible to know

17. 17. Which sequence of transformations could turn a shape into its mirror image facing a different direction?

    • Two translations
    • A reflection followed by a rotation
    • Only a rotation
    • Only a translation

18. 18. If you rotate a shape 90° four times in a row (360° total), the shape ends up:

    • Facing a new direction
    • Back where it started
    • Mirrored
    • Twice the size

19. 19. A point at (2, 3) is translated 3 units right and 2 units down. What are its new coordinates?

    • (5, 1)
    • (5, 5)
    • (-1, 1)
    • (2, 3)

20. 20. Why are translations, reflections and rotations described as preserving a shape's "congruence"?

    • They change the shape's size
    • They keep the shape exactly the same size and form, just repositioned
    • They always create bigger shapes
    • They remove all angles