Question

Suppose you have line AB on a coordinate plane located at A(-3,-4) and B(5,-4). Under a dilation centered at (9,0), line AB becomes like A' B' with coordinates A'(6,-1) and B'(8,-1). What is the scale factor for this dilation?

Answer 1

`(1)/(4)`

Explanation:

Center of dilation: O(9,0).

Line AB with A(-3,-4) and B(5,-4) is dilated with the scale factor k and center of dilation at O to form line A'B' with A'(6,-1) and B'(8,-1).

Then

`OB'=kOB\\ \\OA'=kOA`

Since

`OB'=√((8-9)^2+(-1-0)^2)=√(1+1)=√(2)\\ \\OB=√((5-9)^2+(-4-0)^2)=√(16+16)=4√(2),`

then

`√(2)=k\cdot 4√(2)\\ \\k=(1)/(4)`