Question

Find the co-ordinates of the centroid of \(\triangle \mathrm{PQR}\) whose vertices are \(\mathrm{P}(6, 3), \mathrm{Q}(-2, 5)\) and \(\mathrm{R}(-1, 7)\).

Answer 1

The centroid is $$\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right)$$.

$$G = \left(\frac{6 + (-2) + (-1)}{3}, \frac{3 + 5 + 7}{3}\right)$$

$$= \left(\frac{3}{3}, \frac{15}{3}\right)$$

$$=(1, 5)$$

Hence the centroid is $$G(1, 5)$$.