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"#