Question

Write the coordinates of the circumcentre of a triangle whose centroid and orthocentre are at (3, 3) and (−3, 5), respectively.

Answer 1

Let the coordinates of the circumcentre of the triangle be C(x, y).
Let the points O($-$3, 5) and G(3, 3) represent the coordinates of the orthocentre and centroid, respectively.

We know that the centroid of a triangle divides the line joining the orthocentre and circumcentre in the ratio 2:1.

$$\begin{gathered} \therefore 3=\frac{-3\times 1+2x}{3}\mathrm{and}3=\frac{5\times 1+2y}{3} \\ \Rightarrow x=6,y=2 \end{gathered}$$

Hence, the coordinates of the circumcentre is (6, 2).