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Question

If a triangle has its orthocentre at (1,1) and circumcentre at (32,34), then the coordinates of the centroid of the triangle are


A
(43,56)
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B
(43,56)
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C
(43,56)
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D
(43,56)
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Solution

The correct option is B (43,56)
Given, orthocentre H(1,1) and circumcentre S(32,34)

Let the coordinates of the centroid be (x,y).
We know that, the centroid divides the line segment joining the orthocentre (H) and circumcentre (S) in the ratio 2:1 internally.
So, x=232+112+1=43
and y=234+112+1=56

Coordinates of the centroid are (43,56)

Mathematics

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