Show that the three medians of a triangel go through a common point.?

Question

note: this pint is called the centroid of the triangle

Answer 1

Without loss of generality, the three points are (0,0), (0,2A), and (2B, 2C).

The other ends of the medians are respectively (B, A+C), (B,C), and (0,A).

Well, take two of the lines on which the medians fall, and find their intersection. Check whether that point is also on the third line.

Then there's actually one more step. You've proved that the three lines intersect, but you have to check whether the point of intersection is on the line segments that are the medians.

When you've done that, you're through!

Answer 2

use coordinate geometry to prove it