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Elenna [48]
3 years ago
6

Multiplying a measure by a scale to produce a reduced or enlarged measure

Mathematics
1 answer:
svetoff [14.1K]3 years ago
5 0

Answer:

we conclude that:

  • If the scale factor > 1, the image is stretched
  • If the scale factor < 1, the image is reduced
  • If the scale factor = 1, the image and object will be congruent

Step-by-step explanation:

A dilation is a transformation which generates an image that is the same shape as the original object but in a different size.

The image can be obtained by multiplying the measure of the original object by a scale factor.

If the scale factor > 1, the image is stretched

If the scale factor < 1, the image is reduced

If the scale factor = 1, the image and object will be congruent

For example, if we multiply the measure of the coordinates of the vertex A(2, 2) of a triangle by a scale factor of 2, the image A' is stretched as the scale factor > 1.

Dilation with scale factor 2, multiply by 2.

  • (x, y) → (2x, 2y)

A(2, 2) → (2(2), 2(2)) = A'(4, 4)

So, the image point A'(4, 4) is enlarged.

Dilation with scale factor ½, multiply by ½.

  • (x, y) → (½x, ½y )

A(2, 2) → (2(1/2), 2(1/2)) = A'(1, 1)

So, the image point A'(1, 1) is reduced.

Therefore, we conclude that:

  • If the scale factor > 1, the image is stretched
  • If the scale factor < 1, the image is reduced
  • If the scale factor = 1, the image and object will be congruent

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