Skip to main content
MathidiaMathematics Academy
Transformations
Lesson 52 of 75
Easy practice

Rotations

Objective. Rotate shapes about a given centre.

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

Learn: the key idea

A rotation turns every point of a shape through a fixed angle about a fixed centre, keeping the shape's size and form unchanged. To describe a rotation fully you must state the centre, the angle, and the direction (clockwise or anticlockwise). To rotate a point 90° anticlockwise about the origin, swap the coordinates and negate the new x-value: (x, y) becomes (−y, x). Example: rotating (3, 1) by 90° anticlockwise about the origin gives (−1, 3), which can be checked by tracing a quarter turn on squared paper.

Worked example

Find the image of the point (2, 5) after a rotation of 180° about the origin.

2 … 5
Illustrated card showing 2 … 5
  1. 1A 180° rotation about the origin maps (x, y) to (−x, −y).
  2. 2Apply this rule to the point (2, 5).
  3. 3Negate both coordinates: x becomes −2 and y becomes −5.
  4. 4The image point is (−2, −5).

Answer: (−2, −5)

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 often rotate 90° clockwise when the question says anticlockwise, or vice versa, because they guess the direction instead of tracing it; always sketch or use tracing paper to check the turn direction carefully.

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