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

Question

1445 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-10T02:24:15

Distance moved by centroid $vec(GG') ~~ 8.11$

Dilation factor 5, dilated about D (-1,-2)

Centroid $G = (1+3-1)/3, (5-9-4)/3 => ((1),(-8/3))$

$bar(G'D) = 5 * bar(GD)$

$G'((x+1),(y+2)) = 5 * ((1+1),(-8/3+2)) => ((10),(-10/3))$

$G'((9),(-4/3))$

$vec(G'G) = sqrt((9-1)^2 + (-4/3 + 8/3)^2) ~~ 8.11$

A triangle has corners at (1 ,5 )(1,5)(1 ,5 ), (3 ,-9 )(3,−9)(3 ,-9 ), and (-1 ,-4 )(−1,−4)(-1 ,-4 ). If the triangle is dilated by a factor of 5 55 about point #(-1 ,-2 ), how far will its centroid move?