Question

AB is dilated from the origin to create A'B' at A' (0,6) and B' (6, 9). What scale factor was AB dilated by?

1/2
2
3
4

Answer 1

The scale factor was 3

Explanation:

we know that

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

step 1

Find the distance AB

we have

A(0,2) and B(2,3) -----> see the figure

substitute in the formula

`d=\sqrt{(3-2)^(2)+(2-0)^(2)}`

`d=\sqrt{(1)^(2)+(2)^(2)}`

`AB=√(5)\ units`

step 2

Find the distance A'B'

we have

A'(0,6) and B'(6,9) -----> given value

substitute in the formula

`d=\sqrt{(9-6)^(2)+(6-0)^(2)}`

`d=\sqrt{(3)^(2)+(6)^(2)}`

`A'B'=√(45)\ units`

simplify

`A'B'=3√(5)\ units`

step 3

Find the scale factor

To find out the scale factor divide the length of the image A'B' by the length of the pre-image AB

so

`3√(5)/√(5)=3`

therefore

The scale factor was 3