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:
[tex]k = \frac{9}{3}[/tex]
[tex]k = 3[/tex]
or
[tex]k = \frac{12}{4}[/tex]
[tex]k = 3[/tex]
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:
https://brainly.com/question/13176891
