Suppose HJ is on s coordinate plane located at H(-5,2) and J(1,4). Under a dilation centered at(3,2), HJ becomes H'J' with coordinates H'(-1,2) and J'(2,3). What is the scale factor for this dilation?

1. Find the distance between points H(-5,2) and J(1,4):

[tex]HJ=\sqrt{(-5-1)^2+(2-4)^2}=\sqrt{36+4}=\sqrt{40}=2\sqrt{10}.[/tex]

2. Find the distance between points H'(-1,2) and J'(2,3):

[tex]H'J'=\sqrt{(-1-2)^2+(2-3)^2}=\sqrt{9+1}=\sqrt{10}.[/tex]

3. Consider the ratio

[tex]\dfrac{H'L'}{HL}=\dfrac{\sqrt{10} }{2\sqrt{10} }=\dfrac{1}{2}.[/tex]

Then the scale factor of dilation is [tex]\dfrac{1}{2}.[/tex]