Maths Library

Transformations: Reflection, Rotation, and Translation: Grade 8 math

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 Grade 8 (age 13 to 14) as a main teaching focus. 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 Common Core State Standards. Check wording and codes against the official document.

  • 8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations.

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

Grade 8 math

Qs
6
Marks
6
NameDateScore / 6
1.
The point (2, 2) is translated by 2 right and 1 down. Write the new coordinates.
[1]
2.
The point (4, 3) is translated by 2 left and 3 down. Write the new coordinates.
[1]
3.
The point (4, 1) is translated by 3 right and 3 up. Write the new coordinates.
[1]
4.
The point (3, 2) is translated by 2 right and 1 down. Write the new coordinates.
[1]
5.
The point (3, 2) is translated by 3 left and 1 up. Write the new coordinates.
[1]
6.
The point (4, 4) is translated by 3 left and 1 down. Write the new coordinates.
[1]

Answer key

  1. (4, 1)Add 2 to x and −1 to y; (4, 1)
  2. (2, 0)Add −2 to x and −3 to y; (2, 0)
  3. (7, 4)Add 3 to x and 3 to y; (7, 4)
  4. (5, 1)Add 2 to x and −1 to y; (5, 1)
  5. (0, 3)Add −3 to x and 1 to y; (0, 3)
  6. (1, 3)Add −3 to x and −1 to y; (1, 3)