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

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Answer 1 · 2018-07-14T08:08:00

$color(purple)("Distance moved by centroid "$

$color(blue)(vec(GG') ~~ 28.2843 " units"$

$A(-1,2), B(3,-5), C(7,-3), " about point " D (-2, 4), " dilation factor "5$

Centroid $G(x,y) = ((x_a + x_b + x_c) /3, (y_a + y_b + y_c)/3)$

$G(x,y) = ((-1+3+7)/3, (2 - 5 - 3)/3) = (3, -2)$

$A'((x),(y)) = 5a - 4d = 5*((-1),(2)) - 4*((-2),(4)) = ((3),(18))$

$B'((x),(y)) = 5b - 4d = 5*((3),(-5)) - 4*(-2),(4)) = ((23),(-41))$

$C'((x),(y)) = 5c - 4d = 5*((7),(-3)) - 4*((-2),(4)) = ((43),(-31))$

$"New Centroid " G'(x,y) = ((3+ 23+43)/3,(18- 41-31)/3) = (23,-18)$

$color(purple)("Distance moved by centroid "$

$color(blue)(vec(GG') = sqrt((3-23)^2 + (-2- -18)) ~~ 28.2843 " units"$

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