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

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Answer 1 · 2018-07-14T08:08:00

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

#color(blue)(vec(GG') ~~ 28.2843 " units"#

#A(-1,2), B(3,-5), C(7,-3), " about point " D (-2, 4), " dilation factor "5#

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

#G(x,y) = ((-1+3+7)/3, (2 - 5 - 3)/3) = (3, -2)#

#A'((x),(y)) = 5a - 4d = 5*((-1),(2)) - 4*((-2),(4)) = ((3),(18))#

#B'((x),(y)) = 5b - 4d = 5*((3),(-5)) - 4*(-2),(4)) = ((23),(-41))#

#C'((x),(y)) = 5c - 4d = 5*((7),(-3)) - 4*((-2),(4)) = ((43),(-31))#

#"New Centroid " G'(x,y) = ((3+ 23+43)/3,(18- 41-31)/3) = (23,-18)#

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

#color(blue)(vec(GG') = sqrt((3-23)^2 + (-2- -18)) ~~ 28.2843 " units"#