Find the co-ordinates of the point of intersection of the medians of the triangle whose vertices are A(-7, 5), B(-1, -3) and C(5, 7).

The medians of a triangle intersect at centroid of triangle.

By using the centroid formula,

$(x, y) = \Big(\dfrac{x$1 + x2 + x3}{3}, \dfrac{y1 + y2 + y3}{3} \Big)

A(-7, 5), B(-1, -3) and C(5, 7)

Substitute values we get:

$\Rightarrow (x, y) = \Big( \dfrac{-7 + (-1) + 5}{3}, \dfrac{5 + (-3) + 7}{3} \Big) \\[1em] \Rightarrow (x, y) = \Big( \dfrac{-8 + 5}{3}, \dfrac{5 + 4}{3} \Big) \\[1em] \Rightarrow (x, y) = \Big( \dfrac{-3}{3}, \dfrac{9}{3} \Big) \\[1em] \Rightarrow (x, y) = (-1, 3).$

Hence, co-ordinates of the point of intersection of the medians = (-1, 3).