To find the scale factor of the dilation, we can calculate the distance between the original vertex Q and the new vertex Q'.
Using the distance formula, we have:
d = sqrt((x2-x1)^2 + (y2-y1)^2)
d = sqrt((21-7)^2 + (7-5)^2)
d = sqrt(14^2 + 2^2)
d = sqrt(196 + 4)
d = sqrt(200)
d = 10√2
Since the scale factor is the ratio of the distance between corresponding points in the two polygons, we can calculate the scale factor:
scale factor = d(original) / d(new)
scale factor = 10√2 / 14
scale factor = 5√2 / 7
Therefore, the scale factor of the dilation is 5√2 / 7.
Polygon LMNPQR is shown on the coordinate grid and models the
shape of a garden in a park. Polygon LMNPQR will be dilated with the origin as the center of dilation to create polygon L’M’N’P’Q’R’.
The vertex Q’ will be located at (21, 7).
8.3C_2.JPG
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