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

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Answer 1 · 2018-07-14T01:02:18

$color(purple)(vec(GG') = sqrt((22/3-7)^2 + (5-3)) ~~ 2.0276 " units"$

$A(7,3), B(9,4), C(5,2), " about point " D (6,1), " dilation factor "2$

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

$G(x,y) = ((7+9+5)/3, (3+4+2)/3) = (7, 3)$

$A'((x),(y)) = 2a - d = 2*((7),(3)) - ((6),(1)) = ((8),(5))$

$B'((x),(y)) = 2b - d = 2*((8),(4)) - ((6),(1)) = ((10),(7))$

$C'((x),(y)) = 2c - d = 2*((5),(2)) - ((6),(1) = ((4),(3))$

$"New Centroid " G'(x,y) = ((8+10+4)/3,(5+7+3)/3) = (22/3,5)$

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

$color(purple)(vec(GG') = sqrt((22/3-7)^2 + (5-3)) ~~ 2.0276 " units"$

A triangle has corners at (7 ,3 )(7,3)(7 ,3 ), (9 ,4 )(9,4)(9 ,4 ), and (5 ,2 )(5,2)(5 ,2 ). If the triangle is dilated by a factor of 2 22 about point #(6 ,1 ), how far will its centroid move?