Question

Find the point of the intersection of the medians of a triangle whose vertices are $(-1,0)$, $(5,-2)$ and $(8,2)$

Answer 1

Finding the centroid of the triangle:

The points of the intersection of the medians of a triangle is the centroid.

The formula to find the centroid of a triangle is given as,

$\mathrm{G}=\left(\frac{{\mathrm{x}}_1+{\mathrm{x}}_2+{\mathrm{x}}_3}{3},\frac{{\mathrm{y}}_1+{\mathrm{y}}_2+{\mathrm{y}}_3}{3}\right)$

Where, $\mathrm{G}$ is the centroid of the triangle, $x_1$, $x_2$ and $x_3$ are the $x$-coordinates and $y_1$, $y_2$ and $y_3$ are the $y$-coordinates of the vertices of the triangle.

Thus, the centroid of the given triangle is,

$$\begin{gathered} \mathrm{G}=\left(\frac{-1+5+8}{3},\frac{0+(-2)+2}{3}\right) \\ \mathrm{G}=\left(4,0\right) \end{gathered}$$

Therefore, the point of the intersection of the medians of the given triangle is $(4,0)$.