A triangle has corners at $(5 ,3 )$ , $(9 ,4 )$ , and $(2 ,2 )$ . If the triangle is dilated by a factor of $2$ about point #(9 ,1 ), how far will its centroid move?

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Answer 1 · 2018-07-14T08:21:03

$color(maroon)("Distance moved by centroid " color(indigo)(vec(GG') ~~ 3.6667 " units"$

$A(5,3), B(9,4), C(2,2), " about point " D (9,1), " dilation factor "3$

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

$G(x,y) = ((5+9+2)/3, (3+ 4 + 2)/3) = (16/3, 3)$

$A'((x),(y)) = 2a - d = 2*((5),(3)) - 1*((9),(1)) = ((1),(5))$

$B'((x),(y)) = 2b - d = 2*((9),(4)) - 1*(9),(1)) = ((9),(7))$

$C'((x),(y)) = 2c - d = 2*((2),(2)) - 1*((9),(1)) = ((-5),(3))$

$"New Centroid " G'(x,y) = ((1+ 9- 5)/3,(5+ 7 -3)/3) = (5/3,3)$

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

$color(indigo)(vec(GG') = sqrt((16/3- 5/3)^2 + (3- 3)) ~~ 3.6667 " units"$

A triangle has corners at (5 ,3 )(5 ,3 ), (9 ,4 )(9 ,4 ), and (2 ,2 )(2 ,2 ). If the triangle is dilated by a factor of 2 2 about point #(9 ,1 ), how far will its centroid move?