Question

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?

Answer 1

The dilation is a 1/2

Answer 2

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

`HJ=√((-5-1)^2+(2-4)^2)=√(36+4)=√(40)=2√(10).`

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

`H'J'=√((-1-2)^2+(2-3)^2)=√(9+1)=√(10).`

3. Consider the ratio

`(H'L')/(HL)=(√(10) )/(2√(10) )=(1)/(2).`

Then the scale factor of dilation is
`(1)/(2).`