First slide

Cartesian plane

Question

If the centroid and circumcentre of a triangle are ( 3,3) and ( 6, 2) respectively, then the orthocenire, is

Moderate

A

( - 3 , 5)
B

( - 3 , 1)
C

( 3, - 1)
D

( 9, 5)

Solution

We know that the centroid G(3,3), circumcentre O(6,2) and orthocentre O' (x, y) are collinear such that G divides OO' in the ratio 1 : 2. Therefore,
$3 = \frac{x + 12}{1 + 2}$ and $3 = \frac{y + 4}{1 + 2} \Rightarrow x = - 3$ and $y = 5$
Hence, the coordinates of the orthocentre are ( - 3, 5).

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