Find the coordinates of the point of intersection of the medians of the triangle with the vertices A (2; 1) B (3; 4) C (1; 6)

We are given a triangle with the coordinates of its vertices A (2; 1), B (3; 4) and C (1; 6).

Before we find the point of intersection of the medians, let’s remember what it can be in a triangle.

So, the point of intersection of the medians is the so-called center of gravity of the triangle.

You can calculate the coordinates of the center of gravity by calculating the arithmetic mean of the corresponding coordinates of all three vertices of the triangle.

Let’s write down the coordinates of the center of gravity:

x0 = (xa + xb + xc) / 3 = (2 + 3 + 1) / 3 = 2;

y0 = (ya + yb + yc) / 3 = (1 + 4 + 6) / 3 = 3.

The point of intersection of the medians (2; 3).