Question

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

Answer 1

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

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