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

Answer:

$\dfrac{1}{4}$

Step-by-step 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

$OB'=\sqrt{(8-9)^2+(-1-0)^2}=\sqrt{1+1}=\sqrt{2}\\ \\OB=\sqrt{(5-9)^2+(-4-0)^2}=\sqrt{16+16}=4\sqrt{2},$

then

$\sqrt{2}=k\cdot 4\sqrt{2}\\ \\k=\dfrac{1}{4}$