Answer:
The scale factor of dilation is 2.
Step-by-step explanation:
From the given information it is notices that the vertices of preimage are A(1, 4), B(3, 4), C(3, 1), and D(1, 1). The vertices of image are A'(2, 8), B'(6, 8), C'(6, 2) and D'(2, 2).
The scale factor is the ratio of distance of a image of a vertex from the center of dilation and distance of the vertex from the center of dilation.
The center of dilation is origin. So, the scale factor is
[tex]k=\frac{OA'}{OA}[/tex] .... (1)
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]OA'=\sqrt{(2-0)^2+(8-0)^2}=\sqrt{4+64}=\sqrt{68}=2\sqrt{17}[/tex]
[tex]OA=\sqrt{(1-0)^2+(4-0)^2}=\sqrt{1+16}=\sqrt{17}[/tex]
Now, put these values in equation (1).
[tex]k=\frac{2\sqrt{17}}{\sqrt{17}}[/tex]
[tex]k=2[/tex]
Therefore the scale factor of dilation is 2.
