A triangle has corners at $(-2 ,6 )$ , $(4 ,-3 )$ , and $(2 ,9 )$ . If the triangle is dilated by a factor of $5$ about point #(-7 ,1 ), how far will its centroid move?

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Answer 1 · 2018-06-08T10:57:16

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

$color(crimson)(vec(GG') = 35.9 " units"$

$A(-2,6), B(4,-3), C(2,9), " about point " D (-7,10), " dilation factor "5$

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

$G(x,y) = ((-2+4+2)/3, (6-3+9)/3) = (4/3, 4)$

$A'((x),(y)) = 5a - 4d = 5*((-2),(6)) - 4*((-7),(1)) = ((18),(26))$

$B'((x),(y)) = 5b - 4d = 5*((4),(-3)) - 4*((-7),(1)) = ((48),(-19))$

$A'((x),(y)) = 5c - 4d = 5*((2),(9)) - 4*((-7),(1)) = ((38),(45))$

$"New Centroid " G'(x,y) = ((18+48+38)/3,(26-19+45)/3) = (104/3,52/3)$

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

$color(crimson)(vec(GG') = sqrt((104/3-4/3)^2 + (52/3-4)) = 35.9 " units"$

A triangle has corners at (-2 ,6 )(-2 ,6 ), (4 ,-3 )(4 ,-3 ), and (2 ,9 )(2 ,9 ). If the triangle is dilated by a factor of 5 5 about point #(-7 ,1 ), how far will its centroid move?