A(1,-3) B(2,-4) and A'(4,-12) B'(8,-16)
Determine the scale factor used in the dilation of line segment AB, centered at the origin
1/4
-4
4
2
The scale factor can be determined by comparing the lengths of the line segments before and after the dilation.
Before dilation, the length of line segment AB can be found using the distance formula:
AB = √[(2-1)^2 + (-4-(-3))^2]
= √[1^2 + (-4+3)^2]
= √[1 + 1]
= √2
After the dilation, the length of line segment A'B' can be found using the distance formula:
A'B' = √[(8-4)^2 + (-16-(-12))^2]
= √[4^2 + (-16+12)^2]
= √[16 + (-4)^2]
= √[16 + 16]
= √32
To find the scale factor, we divide the length of A'B' by the length of AB:
Scale factor = A'B' / AB
= √32 / √2
= √(32/2)
= √16
= 4
Therefore, the scale factor used in the dilation of line segment AB, centered at the origin, is 4.