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Section 14.6 · Geometry and measure

Enlargement

Enlarge shapes by a positive integer scale factor about a centre, identify an enlargement, and understand that the image is mathematically similar to the object.

6 teaching slides 58 practice questions Worked answers for every question

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2 · Key words

enlargementA transformation that changes size but not shape.
scale factorThe number every length is multiplied by.
centre of enlargementThe fixed point the enlargement works from.
similarSame shape, possibly different size.
congruentSame shape and same size.
ratioThe comparison of two lengths, unchanged by enlargement.

3 · Summary of the sectionrevise from this

  • An enlargement multiplies every length by a scale factor.
  • It needs two things: the scale factor and the centre of enlargement.
  • From the origin: (x, y) → (kx, ky).
  • From any other centre: multiply the offset from the centre by k, then add the centre back on.
  • Angles do not change. Only lengths do.
  • The image is mathematically similar to the object — same shape, different size. It is not congruent unless k = 1.
  • Lengths and perimeters are multiplied by k.
  • Areas are multiplied by k², because an area is a length times a length.
  • The centre of enlargement is the one point that does not move.
  • A scale drawing is an enlargement — section 14.2 was doing this all along.
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Video lessons1 videos

Enlargements

British corbettmaths

Enlarging from a centre by a whole-number scale factor, and why the image is similar rather than congruent.

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4 · Practice58 questions, easiest first

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