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Question

# If the middle points of the sides of a triangle be (-2, 3), (4,-3) and (4, 5), then the centroid of the triangle is:

A
(5/3,2)
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B
(5/6,1)
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C
(2,5/3)
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D
(1,5/6)
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Solution

## The correct option is C (2,5/3)Let the vertices of the triangle be A(X1,Y1),B(X2,Y2) and C(X3,Y3), then X1+X2=8...............(1)Y1+Y2=10................(2)X2+X3=−4...............(3)Y2+Y3=6..................(4)X3+X1=8...................(5)Y3+Y1=−6.................(6) On solving these equations, we get X1=10,X2=−2,X3=−2,Y1=−1,Y2=11 and Y3=−5 Hence, the centroid is (2, 5/3) Examination method : As we know that the centroid of the triangle ABC and that of the triangle formed by joining the middle points of the sides of triangle BC is same. 4+4−23,5−3+33=(2,53)

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