# Thread: Coordinate Geometry: Finding the centroid of a triangle

1. ## Coordinate Geometry: Finding the centroid of a triangle

The vertices of a triangle are the points P(5,6), Q(-4,3) and R(2,-3). Find the coordinates of the centroid. i.e. the point where the medians meet.

is there an easier way to do this other than the rigorous method of finding the mid point of each side, and then finding the equation of the line and solving simultaenously?

Thank you

2. ## Yes...

Let $A(x_1,y_1)$, $B(x_2,y_2)$ and $C(x_3,y_3)$ points on two dimensional plane.

So, the centroid is given by:

$M(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

Try to prove it, not so hard.

3. Here you can read more about centroid... (really interesting stuff): http://www.mamikon.com/USArticles/EasyCentroids.pdf