Dilations Practice

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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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1 answer

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.
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