Determine the scale factor used in the dilation of line segment AB, centered at the origin.
A = (2,3)
B = (4,1)
A' = (6,9)
B' = (12,3)
-Hiiiiii :)
Hi! To find the scale factor used in the dilation, we can compare the lengths of the original line segment AB and the dilated line segment A'B'.
Using the distance formula, we can find the length of AB:
d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((4 - 2)^2 + (1 - 3)^2)
d = √(2^2 + (-2)^2)
d = √(4 + 4)
d = √8
d = 2√2
Similarly, we can find the length of A'B':
d' = √((12 - 6)^2 + (3 - 9)^2)
d' = √(6^2 + (-6)^2)
d' = √(36 + 36)
d' = √72
d' = 6√2
Now, we can calculate the scale factor by dividing the length of A'B' by the length of AB:
Scale factor = d' / d
Scale factor = (6√2) / (2√2)
Scale factor = 6 / 2 = 3
Therefore, the scale factor used in the dilation of line segment AB is 3.