Maths Library

Transformations: Reflection, Rotation, and Translation: Grade 10 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 10 (age 15 to 16) 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.

  • Represent and compare rigid transformations in the plane such as 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 10 math

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)