A triangle has corners at #(6 ,2 )#, #(5 ,-8 )#, and #(-5 ,3 )#. If the triangle is dilated by a factor of #5 # about point #(7 ,-2 ), how far will its centroid move?

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Answer 1 · 2018-07-14T01:09:58

#color(indigo)(vec(GG') = sqrt((2- -18)^2 + (-1-3)) ~~ 20.396 " units"#

#A(6,2), B(5,-8), C(-5,3), " about point " D (7,-2), " dilation factor "5#

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

#G(x,y) = ((6+5-5)/3, (2-8+3)/3) = (2, -1)#

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

#B'((x),(y)) = 5b - d = 5*((5),(-8)) - 4*((7),(-2)) = ((-3),(-32))#

#C'((x),(y)) = 5c - d = 5*((-5),(3)) - 4*((7),(-2)) = ((-53),(23))#

#"New Centroid " G'(x,y) = ((2-3-53)/3,(18-32+23)/3) = (-18,3)#

#color(indigo)("Distance moved by centroid " #

#color(indigo)(vec(GG') = sqrt((2- -18)^2 + (-1-3)) ~~ 20.396 " units"#