A triangle has corners at $(-2 ,1 )$ , $(6 ,-3 )$ , and $(-1 ,4 )$ . If the triangle is dilated by a factor of $5$ about point #(4 ,-9 ), how far will its centroid move?

Question

1429 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-14T00:53:31

$color(crimson)(vec(GG') = sqrt((-1/3-1)^2 + (118/3-2/3)) ~~ 38.69 " units"$

$A(-2,1), B(6,-3), C(-1,4), " about point " D (4,-9), " dilation factor "5$

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

$G(x,y) = ((-2+6-1)/3, (1 - 3 + 4)/3) = (1, 2/3)$

$A'((x),(y)) = 5a - 4d = 5*((-2),(1)) - 4*((4),(-9)) = ((-26),(41))$

$B'((x),(y)) = 5b - 4d = 5*((6),(-3)) - 4*((4),(-9)) = ((14),(21))$

$C'((x),(y)) = 5c - 4d = 5*((-1),(4)) - 4*((4),(-9)) = ((11),(56))$

$"New Centroid " G'(x,y) = ((-26+14+11)/3,(41+21+56)/3) = (-1/3,118/3)$

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

$color(crimson)(vec(GG') = sqrt((-1/3-1)^2 + (118/3-2/3)) ~~ 38.69 " units"$

A triangle has corners at (-2 ,1 )(-2 ,1 ), (6 ,-3 )(6 ,-3 ), and (-1 ,4 )(-1 ,4 ). If the triangle is dilated by a factor of 5 5 about point #(4 ,-9 ), how far will its centroid move?