A triangle has corners at (6 ,3 ), (4 ,-1 ), and (2 ,-9 ). If the triangle is dilated by a factor of 5 about point #(2 ,-4 ), how far will its centroid move?

1 Answer
Leland Adriano Alejandro
Mar 24, 2016

It will move by distance=4/3sqrt61=10.4137" "units

Explanation:

We need to compute the old centroid and the new centroid first.

We compute the old centroid (x_c, y_x) first

x_c=(x_1+x_2+x_3)/3=(6+2+4)/3=4

y_c=(y_1+y_2+y_3)/3=(3+(-9)+(-1))/3=-7/3

Old centroid (x_c, y_x)=(4, -7/3)

Now we compute the new centroid (x_c', y_c')

The given problem is about dilated by a factor of 5, therefore the ratio of the distance of the new centroid from the reference point (2, -4) to the distance of the old centroid from the reference point is 5:1

For x_c'

(x_c'-2)/(x_c-2)=5/1

(x_c'-2)/(4-2)=5/1

x_c'=12

For y_c'

(y_c'--4)/(y_c--4)=5/1

(y_c'--4)/(-7/3--4)=5/1

y_c'=13/3

New centroid (x_c', y_c')=(12, 13/3)

Distance d from old centroid to the new centroid

d=sqrt((x_c-x_c')^2+(y_c-y_c')^2)

d=sqrt((4-12)^2+(-7/3-13/3)^2)

d=sqrt(976/9)=4/3sqrt(61)=10.4137

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

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