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Question

Find the centroid of the triangle with vertices A(x1,y1), B(x2,y2) and C(x3,y3).


A

(x1+ x2+ x­3)/3 , (y1+ y2+ y3)/3

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B

- (x1+ x2+ x­3)/3 , - (y1+ y2+ y3)/3

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C

(x1 - x2 - x­3)/3 , (y1- y2 - y3)/3

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D

(x1- x2+ x­3)/3 , (y1- y2+ y3)/3

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Solution

The correct option is A

(x1+ x2+ x­3)/3 , (y1+ y2+ y3)/3


Draw the median AD. D is the midpoint of BC. So D is x2+x32,y2+y32.

Let G be the centroid. It divides AD in the ratio 2:1. So using the section formula with m = 2 and n =1

This is an important result to remember. Observe that the formula for the centroid is symmetric with respect to x1,x2,x3,y1,y2,y3 so it doesn't matter in what order the vertices are taken.

(x1+x2+x3)3,(y1+y2+y3)3.


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