Question

What is the scale factor of the dilation?

Answer 1

Answer:

The scale factor of the dilation is 3.

Step-by-step explanation:

The scale factor of the dilation is

$k=\frac{\text{Side of image}}{\text{Corresponding side of preimage}}$

$k=\frac{A'B'}{AB}$             ... (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

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$A'B'=\sqrt{(12-3)^2+(15-15)^2}=9$

The coordinates of A and B are (1,5) and (4,5).

$AB=\sqrt{(4-1)^2+(5-5)^2}=3$

Substitute A'B'=9 and AB=3 in equation (1).

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

$k=3$

Therefore the scale factor of the dilation is 3.

Answer 2

Answer:

3

Step-by-step explanation:

D(1 , 1) to D'(3, 3)

so x (1 x 3)= 3

    y (1 x 3) = 3

SF = 3

D(1 , 5) to D'(3, 15)

so x (1 x 3)= 3

    y (5 x 3 ) = 15

SF = 3

Same on coordinate points B to B' and C to C'

so SF = 3