A triangle has corners at $(6, 2)$ $(6 ,2 )$ , $(5, - 8)$ $(5 ,-8 )$ , and $(- 5, 3)$ $(-5 ,3 )$ . If the triangle is dilated by a factor of $5$ $5$ about point #(7 ,-2 ), how far will its centroid move?

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Answer 1 · 2018-07-14T01:09:58

$color(indigo)(vec(GG') = sqrt((2- -18)^2 + (-1-3)) ~~ 20.396 " units"$

$A(6,2), B(5,-8), C(-5,3), " about point " D (7,-2), " dilation factor "5$

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

$G(x,y) = ((6+5-5)/3, (2-8+3)/3) = (2, -1)$

$A'((x),(y)) = 5a - d = 5*((6),(2)) - 4*((7),(-2)) = ((2),(18))$

$B'((x),(y)) = 5b - d = 5*((5),(-8)) - 4*((7),(-2)) = ((-3),(-32))$

$C'((x),(y)) = 5c - d = 5*((-5),(3)) - 4*((7),(-2)) = ((-53),(23))$

$"New Centroid " G'(x,y) = ((2-3-53)/3,(18-32+23)/3) = (-18,3)$

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

$color(indigo)(vec(GG') = sqrt((2- -18)^2 + (-1-3)) ~~ 20.396 " units"$

A triangle has corners at (6 ,2 )(6,2)(6 ,2 ), (5 ,-8 )(5,−8)(5 ,-8 ), and (-5 ,3 )(−5,3)(-5 ,3 ). If the triangle is dilated by a factor of 5 55 about point #(7 ,-2 ), how far will its centroid move?