A triangle has corners at $(3 ,1 )$ , $(1 ,-2 )$ , and $(-4 ,-5 )$ . If the triangle is dilated by a factor of $5$ about point #(7 ,-6 ), how far will its centroid move?

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Answer 1 · 2018-04-21T09:23:11

$4 sqrt{65}$

The centroid is the center of mass of the triangle and is given by the average of the coordinates:

$C=\frac 1 3(3+1-4,1-2-5)=(0,-2)$

The distance from the centroid to the dilation point $(7,-6)$ is

$d = \sqrt{(0-7)^2+(-2 - -6)^2} = sqrt{65}$

The factor of five dilation means this will end up $5 sqrt{65}$ from the dilation point after dilation, so will have moved $4 sqrt{65}$ .

A triangle has corners at (3 ,1 )(3 ,1 ), (1 ,-2 )(1 ,-2 ), and (-4 ,-5 )(-4 ,-5 ). If the triangle is dilated by a factor of 5 5 about point #(7 ,-6 ), how far will its centroid move?