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?

Question

asked May 7, 2022 26.0k views

1 Answer

MikeVelazco · Answer 1 · 2022-05-13T11:00:06+0000

Answer:

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