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?

1 Answer
Dean R.
Apr 21, 2018

4 sqrt{65} 4√65

Explanation:

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)C=13(3+1−4,1−2−5)=(0,−2)

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

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

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

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