Question

If the centroid and circumcentre of triangle are (3, 3); (6, 2), then the orthocentre is

• A. (9, 5)
• B. (3, –1)
• C. (– 3, 1)
• D. (– 3, 5)

Answer 1

Answer: (D)

(– 3, 5)

Answer 2

Let orthocentre be $(\alpha,\beta)$. We know that centroid divides the line joining orthocentre and circumcentre in the ratio 2 : 1

∴$3 = \frac{2(6) + 1(\alpha)}{2 + 1} \Rightarrow \alpha = - 3$, $3 = \frac{2(2) + 1(\beta)}{2 + 1} \Rightarrow \beta = 5$

Hence orthocentre is (–3, 5).