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

1 Answer
Leland Adriano Alejandro
Nov 22, 2016

the centroid will move by about (8sqrt(5))/5
Delta=(8sqrt(5))/5

Delta=3.5771" "units

Explanation:

the solution:

the centroid of the given triangle is at
x_o=(-4+7+2)/3=5/3

y_o=(2+1-7)/3=-4/3

the reference point is at (-1, 4)" "and scale factor k=2/5

Let the unknown new centroid be at C(x_c, y_c)

By segment division method

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

(x_c-(-1))/(5/3-(-1))=2/5

x_c=1/15

Also

(y_c-4)/(y_o-4)=2/5

(y_c-4)/(-4/3-4)=2/5

y_c=28/15

The old centroid is at (5/3, -4/3)" "(black colored dot)
The new centroid is at C(1/15, 28/15)" "(orange colored dot)

![Desmos.com](useruploads.socratic.org)

how far did the centroid move ?

Delta=sqrt((x_o-x_c)^2 + (y_o-y_c)^2)

Delta=sqrt((5/3-1/15)^2 + (-4/3-28/15)^2)

Delta=sqrt((64+256)/25)

Delta=(8sqrt(5))/5

Delta=3.5771" "units (length of the green segment)

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

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