A triangle as corners at $(2 ,7 )$ , $(5 ,8 )$ , and $(3 ,1 )$ . If the triangle is dilated by a factor of $3$ about #(6 ,5 ), how far will its centroid move?

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Answer 1 · 2018-07-14T08:15:12

$color(maroon)("Distance moved by centroid " color(green)(vec(GG') ~~ 1.4907 " units"$

$A(2,7), B(5,8), C(3,1), " about point " D (6,5), " dilation factor "3$

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

$G(x,y) = ((2+5+3)/3, (7+ 8 + 1)/3) = (10/3, -16/3)$

$A'((x),(y)) = 3a - 2d = 3*((2),(7)) - 2*((6),(5)) = ((-6),(11))$

$B'((x),(y)) = 3b - 2d = 3*((5),(8)) - 2*(6),(5)) = ((3),(14))$

$C'((x),(y)) = 3c - 2d = 3*((3),(1)) - 2*((6),(5)) = ((-3),(-7))$

$"New Centroid " G'(x,y) = ((-6+ 3- 3)/3,(11+ 14 -7)/3) = (-2,6)$

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

$color(green)(vec(GG') = sqrt((10/3- -2)^2 + (-16/3- 6)) ~~ 1.4907 " units"$

A triangle as corners at (2 ,7 )(2 ,7 ), (5 ,8 )(5 ,8 ), and (3 ,1 )(3 ,1 ). If the triangle is dilated by a factor of 3 3 about #(6 ,5 ), how far will its centroid move?