Question

What is the scale factor of the dilation?

Answer 1

3

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

Answer 2

The scale factor of the dilation is 3.

Explanation:

The scale factor of the dilation is

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

`k=(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=√((x_2-x_1)^2+(y_2-y_1)^2)`

`A'B'=√((12-3)^2+(15-15)^2)=9`

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

`AB=√((4-1)^2+(5-5)^2)=3`

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

`k=(9)/(3)`

`k=3`

Therefore the scale factor of the dilation is 3.