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MathidiaMathematics Academy
Transformations
Lesson 54 of 75
Challenge

Enlargement

Objective. Enlarge shapes from a centre using positive scale factors.

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

Learn: the key idea

An enlargement resizes a shape from a fixed centre by a scale factor, keeping angles the same but multiplying every length from the centre by that factor. For a positive scale factor greater than 1 the image is bigger; between 0 and 1 the image is smaller. To enlarge a point from a centre, find the vector from the centre to the point, multiply it by the scale factor, then add it back to the centre. Example: enlarging (4, 2) from centre (0, 0) by scale factor 3 gives (12, 6), since each coordinate is simply multiplied by 3.

Worked example

Enlarge the point (5, 3) from the centre (1, 1) using a scale factor of 2.

5 … 3
Illustrated card showing 5 … 3
  1. 1Find the vector from centre to point: (5 − 1, 3 − 1) = (4, 2).
  2. 2Multiply this vector by the scale factor 2, giving (8, 4).
  3. 3Add this scaled vector back to the centre coordinates.
  4. 4The image is (1 + 8, 1 + 4) = (9, 5).

Answer: (9, 5)

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Common mistake. Pupils often forget to measure from the centre of enlargement and instead multiply coordinates directly from the origin; when the centre isn't the origin, subtract the centre first, scale, then add the centre back.

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