Question

Mrs. Sloan draws two figures on the board.

Answer 1

A dilated shape will either be enlarged or compressed.

Allen did not make any mistake, and the scale factor is 3.

The dimension of the smaller rectangle (figure Z) is:

3 units by 4 units

The corresponding dimension of the bigger rectangle (figure Z') is:

9 units by 12 units

The scale factor (k) is calculated by dividing the dimensions of Z' by Z.

So, we have:

$k = \frac{9}{3}$

$k = 3$

or

$k = \frac{12}{4}$

$k = 3$

Notice that both values of k are the same (i.e. 3)

This means that the scale factor is 3

Also figure Z and Z' share the same center of origin at point X

This means that the center of dilation from Z to Z' is X

Hence,

Allen made no mistake, and she is correct about the scale factor.

Read more about dilations at:

brainly.com/question/13176891