determine the scale factor used in the dilation of like segment AB, centered at the origin.
A (2,3), B (4,1)
A' (6,9), B' (12,3)
To find the scale factor used in the dilation, we can compare the lengths of the corresponding sides of the original segment and the dilated segment.
The length of AB can be found using the distance formula:
AB = √((4 - 2)^2 + (1 - 3)^2)
= √(2^2 + (-2)^2)
= √(4 + 4)
= √8
= 2√2
The length of A'B' can also be found using the distance formula:
A'B' = √((12 - 6)^2 + (3 - 9)^2)
= √(6^2 + (-6)^2)
= √(36 + 36)
= √72
= 6√2
Therefore, the scale factor used in the dilation is the ratio of the length of the dilated segment to the length of the original segment:
Scale factor = A'B' / AB
= (6√2) / (2√2)
= 3
The scale factor used in the dilation of segment AB is 3.