A triangle has corners at (-2 ,3 ), (3 ,6 ), and (8 ,-6 ). If the triangle is dilated by a factor of 2 about point #(1 ,2 ), how far will its centroid move?

1 Answer

The new centroid (5, 0)

Explanation:

Compute centroid of the original triangle with corners P_1(-2, 3) and
P_2(3, 6) and P_3(8, -6) with reference point (1, 2)

barx=(x_1+x_2+x_3)/3=(-2+3+8)/3=3

bary=(y_1+y_2+y_3)/3=(3+6-6)/3=1

Compute centroid of the new triangle (x, y) using ratio 2:1

(x-1)/(3-1)=2/1

x-1=2*2

x=5

(y-2)/(1-2)=2/1

y-2=-1*2

y=0

The new centroid (5, 0)

God bless....I hope the explanation is useful.