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

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=2⋅32+1⋅12+1=43 and y=2⋅34+1⋅12+1=56 ∴ Coordinates of the centroid are (43,56)Mathematics

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