Maths Library

Transformations: Reflection, Rotation and Translation: Year 11 maths

This topic covers transforming 2D shapes on a coordinate grid via reflection, rotation, and translation. The worksheet practises carrying out transformations and describing transformations that map an object onto its image.

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What this covers

Transformations: Reflection, Rotation and Translation is taught in Year 11 (age 15 to 16, KS4) as a topic to introduce. It sits in the Geometry strand.

Worked example

Translate the point (3, 5) by the vector [2, -4].

  1. Add the x-shift to the x-coordinate: 3 + 2 = 5
  2. Add the y-shift to the y-coordinate: 5 + (-4) = 1
  3. Combine into new coordinates: (5, 1)

Answer: (5, 1)

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Translations described in words (e.g. 3 right, 2 up)
  2. Reflections in horizontal or vertical lines (x = a, y = b)
  3. Rotations of 90 or 180 degrees about the origin
  4. Translations using column vectors and reflections in y = x
  5. Fully describing a single transformation between two drawn shapes

Common mistakes

  • Mixing up the order of coordinates or direction of vector components (x vs y)
  • Confusing clockwise and anticlockwise directions during rotation

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Describe and execute translations, rotations, reflections, and enlargements.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Transformations: Reflection, Rotation and Translation

Year 11 maths

Qs
6
Marks
24
NameDateScore / 24
1.
The point (2, 2) is translated by 2 right and 1 down. Write the new coordinates.
[4]
2.
Reflect the point (4, 3) in the x-axis.
[4]
3.
The point (4, 1) is translated by 3 right and 3 up. Write the new coordinates.
[4]
4.
Reflect the point (3, 2) in the y-axis.
[4]
5.
Reflect the point (3, 2) in the y-axis.
[4]
6.
Reflect the point (4, 4) in the y-axis.
[4]

Answer key

  1. (4, 1)Add 2 to x and −1 to y; (4, 1)
  2. (4, −3)A reflection in the x-axis changes the sign of y; (4, −3)
  3. (7, 4)Add 3 to x and 3 to y; (7, 4)
  4. (−3, 2)A reflection in the y-axis changes the sign of x; (−3, 2)
  5. (−3, 2)A reflection in the y-axis changes the sign of x; (−3, 2)
  6. (−4, 4)A reflection in the y-axis changes the sign of x; (−4, 4)