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Enlargements

Enlargements. Last one of these - honest. Most complicated transformation. Can make the shape larger or smaller in size. The position of the centre of enlargement determines where the image will be, the scale factor determines the size. Keywords.

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Enlargements

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  1. Enlargements Last one of these - honest

  2. Most complicated transformation • Can make the shape larger or smaller in size. • The position of the centre of enlargement determines where the image will be, the scale factor determines the size.

  3. Keywords • Scale factor – the amount of times the lengths of the shape are increased by. • Centre of enlargement – the point the enlargement takes place from

  4. Simplest case No centre of enlargement, just make the shape bigger

  5. Enlarge shape by a scale factor of 3 Object image Just make all the lengths 3 times longer.

  6. That wasn’t difficult. Well let’s add the centre of enlargement

  7. Enlarge the object by a scale factor of 2 from the centre of enlargement object image A A’ o B C B’ C’ oB’ = 2oB A’B’ = 2AB

  8. That wasn’t easy! • Measure the distance from the centre of enlargement to the first corner of the object. • Double this distance (for scale factor 2) and then draw a line that long from the c. of E. passing through the point on the object. • At the end of this line is the corresponding point on the image. • Repeat for the remaining points.

  9. o From o to A = 3cm so oA’ will be 6cm. Draw a 6cm line from o passing through A. At the end of this line is A’ Repeat for the other points. Show me.Enlarge shape by s.f. of 2 3cm 6cm A A’

  10. A few more important points Don’t rub out your construction lines

  11. If a shape is enlarged by a scale factor,k, then the area of the image is k2larger than that of the object. Almost there now

  12. The inverse of an enlargement of scale factor, k is…. An enlargement of scale factor 1/k from the same centre of enlargement. If the scale factor was 2/3 the inverse would be an enlargement by a scale factor of 3/2

  13. The end Any questions?

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