A triangle has corners at #(-2 ,1 )#, #(8 ,-5 )#, and #(-3 ,-2 )#. If the triangle is dilated by a factor of #5 # about point #(7 ,5 ), how far will its centroid move?

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Answer 1 · 2018-06-08T02:35:38

#"Centroid " color(purple)( G" has moved by " = 34.42" units to G' "#

#A (-2,1), b(8,-5), C(-3,-2), D(7,5) "dilation factor ' 5#

Centroid #G = (x_1 + x_2 + x_3) /3, (y_1 + y_2 + y_3) / 3#

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

#A' ((x),(y)) = 5a - 4d = 5*((-2),(1)) - 4*(7),(5)) = ((-38, 15)#

#B' ((x),(y)) = 5b - 4d = 5*((8),(-5)) - 4*(7),(5)) = ((12, -45)#

#C' ((x),(y)) = 5c - 4d = 5*((-3),(-2)) - 4*(7),(5)) = ((-43, -38)#

#G'(x,y) = ((-38 + 12 -43) / 3, (15 - 45 - 38)/3) = (-23, 68/3)#

#color(purple)(bar(GG') = sqrt((-23-1)^2 + (68/3+2)^2) = 34.42# units