Question

A dilation maps AB onto A'B'. If the coordinates of the

endpoints are

A(4,2),
A'(10,5),
B(10,6),
B'(25, 15), then
what is the scale factor?

Answer 1

`k = 2.5`

Explanation:

Given

`A = (4,2)`

`A' = (10,5)`

`B = (10,6)`

`B' = (25,15)`

Required

Determine the scale factor (k)

Scale factor is calculated using:

`Old * k = New`

In this case, we have:

`AB* k = A'B'`

Make k the subject

`k = (A'B')/(AB)`

Using point A and A'

`k = (A')/(A)`

`k = ((10,5))/((4,2))`

Factorize the numerator

`k = (2.5(4,2))/((4,2))`

`k = 2.5*((4,2))/((4,2))`

`k = 2.5*1`

`k = 2.5`