Question

Given a point A(-3,-1), it is dilated by some scale

factor to A' (-9,-3). If the same dilation is applied
to B(-1,-5), what are the coordinates of B'?

Answer 1

`B' = (-3, -15)`

Explanation:

Given

`A = (-3,-1)`

`A' = (-9,-3)`

`B = (-1,-5)`

Required

Determine the coordinates of B'

Since A' is the image of A; we need to first calculate the scale factor using

`A' = A * Scale\ factor`

Make Scale Factor the subject

`Scale\ Factor = (A')/(A)`

Substitute values for A' and A

`Scale\ Factor = ((-9,-3))/((-3, -1))`

Factorize the numerator

`Scale\ Factor = (3 * (-3,-1))/((-3, -1))`

`Scale\ Factor = (3 * 1)/(1)`

`Scale\ Factor = 3`

The coordinates of B' is then calculated as follows:

`B' = B * Scale\ Factor`

Substitute values for B and Scale Factor

`B' = (-1,-5) * 3`

`B' = (-3, -15)`