To determine the scale factor, we can compare the distances between the original points and the corresponding points after dilation.
The distance between point A and the origin is sqrt((-3-0)^2 + (4-0)^2) = 5.
The distance between point A' and the origin is sqrt((-6-0)^2 + (8-0)^2) = 10.
Therefore, the scale factor is 10/5 = 2.
The scale factor used in the dilation of line AB, with a center point of dilation at the origin, is 2.
Dilations Practice
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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)
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