To find the scale factor, we need to compare the lengths of line AB and line A' B'.
The length of line AB can be found using the distance formula:
AB = √((x2 - x1)^2 + (y2 - y1)^2)
= √((2 - (-3))^2 + (-4 - 4)^2)
= √((5)^2 + (-8)^2)
= √(25 + 64)
= √89
The length of line A' B' can also be found using the distance formula:
A' B' = √((x2 - x1)^2 + (y2 - y1)^2)
= √((4 - (-6))^2 + (-8 - 8)^2)
= √((10)^2 + (-16)^2)
= √(100 + 256)
= √356
So, the scale factor is:
Scale factor = A' B' / AB
= √356 / √89
= √4 * √89 / √89
= 2
Therefore, the scale factor used in the dilation of line AB, with a center point of dilation at the origin, is 2.
Dilations Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
Use the image to answer the question.
A coordinate plane with four quadrants shows an x axis capped with arrows and ranging from negative 11 to 10 in 1 unit increments and a y axis capped with arrows and ranging from 12 to negative 12 in 1 unit increments. Points upper A, upper B, upper A prime, and upper B prime are plotted. A coordinate plane with four quadrants shows an x axis capped with arrows and ranging from negative 11 to 10 in 1 unit increments and a y axis capped with arrows and ranging from 12 to negative 12 in 1 unit increments. Point upper A is plotted as left parenthesis negative 3 comma 4 right parenthesis and point upper B is plotted as left parenthesis 2 comma negative 4 right parenthesis. The points are joined by a line that extends beyond the points and is capped with arrows at both ends. Point upper A prime is plotted as left parenthesis negative 6 comma 8 right parenthesis and point upper B prime is plotted as left parenthesis 4 comma negative 8 right parenthesis. The points are joined by a line that extends beyond the points and is capped with arrows at both ends.
Determine the scale factor used in the dilation of line AB , with a center point of dilation at the origin.
(1 point)
The scale factor is
.
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