The scale factor used in the dilation of line AB, with a center point of dilation at the origin, can be determined by comparing the lengths of the original line AB and the dilated line A' B'.
The length of line AB can be calculated using the distance formula:
AB = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) = (9, 9) and (x2, y2) = (6, 6)
AB = √((6 - 9)^2 + (6 - 9)^2)
= √((-3)^2 + (-3)^2)
= √(9 + 9)
= √18
= 3√2
Similarly, the length of line A' B' can be calculated using the distance formula:
A'B' = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) = (3, 3) and (x2, y2) = (2, 2)
A'B' = √((2 - 3)^2 + (2 - 3)^2)
= √((-1)^2 + (-1)^2)
= √(1 + 1)
= √2
Therefore, the scale factor used in the dilation is:
3√2 / √2 = 3
Use the image to answer the question.
A coordinate plane with four quadrants shows an x axis capped with arrows and ranging from negative 3 to 12 in 1 unit increments and a y axis capped with arrows and ranging from 15 to negative 4 in 1 unit increments. Points upper A, upper B, upper A prime, and upper B prime are plotted in quadrant 1. A coordinate plane with four quadrants shows an x axis capped with arrows and ranging from negative 3 to 12 in 1 unit increments and a y axis capped with arrows and ranging from 15 to negative 4 in 1 unit increments. Point upper A is plotted as left parenthesis 9 comma 9 right parenthesis and point upper B is plotted as left parenthesis 6 comma 6 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 3 comma 3 right parenthesis and upper B prime is plotted as left parenthesis 2 comma 2 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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