Question

For the following, find the scale factor if ▼A is the original image. If your answer is a fraction, put a slash between the numbers.

Scale factor = ______

Answer 1

3/2 (see comment)

Explanation:

You want the scale factor relating image triangle B to original triangle A.

Scale factor

Triangle B is an isosceles right triangle with sides of 3 units. Triangle A is an isosceles right triangle with sides of 2 units. The scale factor of the two triangles is ...

(B size)/(A size) = 3/2

The scale factor is 3/2.

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Additional comment

Triangle B can be obtained from triangle A by dilation about the point (1, 1) using a scale factor of -3/2. The negative scale factor reflects the image across the center of dilation, in addition to changing its size.

The same effect can be achieved by dilation by a factor of 3/2, then rotating the figure 180° (or reflecting it across the x- and y-axes), and translating it to its final position.

Whether you call the scale factor 3/2 or -3/2 depends on how it fits into the transformation of ∆A to ∆B.

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