Question

suppose you have ab on a coordinate plane located at a(-3,-4) and b(5,-4). under a dilation centered at (9,0), ab becomes a'b' with coordinates A'(6,-1) and B'(8,-1). What is the scale factor for this dilation

Answer 1

A. 1/4

Explanation:

i did it just now and got it right

Answer 2

The distace between the center of dilation and point a is diven by:


`d=√((9-(-3))^2+(0-(-4))^2) \\ \\ =√((9+3)^2+(0+4)^2)=√(12^2+4^2) \\ \\ =√(144+16)=√(160)=√(16*10)=4√(10)`

The distance between the center of dilation and point a' is given by:


`d=√((9-6)^2+(0-(-1))^2) \\ \\ =√(3^2+(0+1)^2)=√(3^2+1^2) \\ \\ =√(9+1)=√(10)`

It can be seen that the distance from the center of dilation to the image is 1/4 times the distance from the centre of dilation to the preimage.

Therefore, the scale factor is 1/4.