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| Enlargement or Dilatation |
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Let us construct  |
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| Take any point x. |
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 |
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| Join XA, XB, XC and produce them to points P, Q, R respectively, such that |
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| XP = 3XA |
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| XQ = 3XB |
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| XR = 3XC |
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| Join PQ, QR and PR |
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 |
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 The sides of the  are three times the corresponding sides of  |
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The sides of the  are parallel to the sides of  |
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| The point X is called the centre of enlargement. |
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| Let us consider various cases for different values of the enlargement factor. |
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 |
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| Enlargement factor greater than one. |
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| when K > 1 |
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| Let K = 2 |
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| Take O as the centre of enlargement, two possible figures are shown: |
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  |
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 (Pre-image) |
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| AB = 3 cm |
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| BC = 4.2 cm |
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| AC = 6 cm |
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 image |
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| PQ = 6 cm |
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| QR = 8.4 cm |
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| PR = 12 cm |
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  |
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| Enlargement factor less than one. |
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| when K < 1 |
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| Let K = 1/3 |
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| In this case two possible figures are as shown: |
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  |
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 (Pre-image) |
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| AB = 4.5 cm |
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| BC = 6 cm |
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| AC = 7.5 cm |
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 (Image) |
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| PQ = 1.5 cm |
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| QR = 2.0 cm |
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| PR = 2.5 cm |
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| Enlargement factor equal to one. |
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| when K = 1 |
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  |
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| DABC (Pre-image)
DPQR (Image) |
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| AB = 2 cm PQ = 2 cm |
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| BC = 3 cm QR = 3 cm |
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| AC = 3.5 cm PR = 3.5 cm |
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| To Summarise |
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| (1) In case (iii) DABC is
an image of itself. |
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| (2) When K = 1, we get congruent figures and congruent figures are also similar. |
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| (3) In each case, image is similar to pre-image. |
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| (4) The ratio of corresponding sides is K. |
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| (5) The corresponding sides are parallel to each other. |
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| (6) The ratio of the areas of two similar figures is K2. |
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| (7) In solids, the ratio of the volumes of two similar solids will be K3. |
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