Question

Rectangle ABCD is transformed to AB’C’D’ by a dilation .What is the scale factor used for the dilation ?

Answer 1

the scale factor should be 3

Answer 2

Answer:  The required scale factor that is used for the dilation is 3.

Step-by-step explanation:  Given that the rectangle ABCD is transformed to A'B'C'D' by a dilation.

We are to find the scale factor that is used for the dilation.

We know that

the scale factor of dilation is defined as

$S=\dfrac{\textup{the length of a side of the dilated figure}}{\textup{the length of the corresponding side of the original figure}}.$

From the graph, we see that

in rectangle ABCD, the length the side AB is 2 units

and

the length of the corresponding side A'B' in the dilated rectangle A'B'C'D' is 6 units.

Therefore, the scale factor of dilation is given by

$S=\dfrac{A'B'}{AB}=\dfrac{6}{2}=3.$

Thus, the required scale factor that is used for the dilation is 3.