Skip to main content
MathidiaMathematics Academy
Transformations and vectors
Lesson 60 of 75
Review

Transformation invariants

Objective. Compare which properties transformations preserve.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Transformation invariants are the properties of a shape that stay unchanged after a particular transformation is applied, which helps distinguish between types of transformation. Translation and rotation preserve both the size and shape of an object exactly, including all side lengths and angles, so the image is congruent to the original. Reflection also preserves size and shape but reverses the shape's orientation, like a mirror image. Enlargement is different because it preserves angles and the overall shape, but not the side lengths, unless the scale factor is exactly 1 or −1.

Worked example

Which transformation preserves both the size and the orientation of a shape? Choose the correct transformation.

Options
  • Reflection
  • Enlargement
  • Translation
  • Shearing
  1. 1Reflection preserves size but reverses orientation, so it is not the answer.
  2. 2Enlargement changes size (unless scale factor is 1), so it is not the answer.
  3. 3Rotation preserves both size and keeps the shape's orientation consistent with the turn.
  4. 4Translation also preserves both size and orientation, since it only slides the shape.

Answer: Translation

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Pupils sometimes assume enlargement preserves side lengths just like other transformations, forgetting that only angles and shape are preserved while lengths change by the scale factor. Remember enlargement changes size unless the scale factor is 1 or −1.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard