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Question

If the orthocentre, circumcentre of a triangle are (−3,5,2),(6,2,5) respectively, then the centroid of the triangle is

A
(3,3,4)
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B
(32,72,92)
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C
(9,9,12)
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D
(92,32,32)
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Solution

The correct option is A (3,3,4)
Circumcentre =(6,2,5)
Orthocenter =(3,5,2)
As we know that centroid divides the line joining orthocentre and circumcentre in ratio 2:1.
Therefore, on applying section formula,
Centroid =(1×(3)+2×62+1,1×5+2×22+1,1×2+2×52+1)=(3+123,5+43,2+103)=(3,3,4)

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