Question

If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?

Answer 1

Answer:

The scale factor is 1.

Step-by-step explanation:

Let k be the scale factor of a dilation of triangle ABC to form the image triangle A'B'C'.

The dilation is a magnification if

$|k| > 1$

In this case, the preimage will be similar to the image triangle.

If

$- 1\: < \: k \: < \: 0 \: \: or \: \: 0 \: < \: k \: < \: 1$

the dilation is a reduction. The image and pre-image will still be similar.

But if

$k = 1$

the image is the same as the preimage.

We say the pre-image is congruent to the image triangle.