Answer:
The scale factor of the dilation is 3.
Step-by-step explanation:
The scale factor of the dilation is
[tex]k=\frac{\text{Side of image}}{\text{Corresponding side of preimage}}[/tex]
[tex]k=\frac{A'B'}{AB}[/tex] ... (1)
From the given figure it is clear that the coordinates of A' and B' are (3,15) and (12,15).
Using distance formula we get
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]A'B'=\sqrt{(12-3)^2+(15-15)^2}=9[/tex]
The coordinates of A and B are (1,5) and (4,5).
[tex]AB=\sqrt{(4-1)^2+(5-5)^2}=3[/tex]
Substitute A'B'=9 and AB=3 in equation (1).
[tex]k=\frac{9}{3}[/tex]
[tex]k=3[/tex]
Therefore the scale factor of the dilation is 3.
