Consider one specific triangle ABC with A = (4,8), B = (2,-6), and C = (-4,4). The three medians of this triangle meet at a point. What is that point?

1 Answer
Nov 16, 2017

Centroid of a triangle whose three vertices are (4,8),(2,-6) and (-4,4) is (2/3,2)

Explanation:

Median is the line joining a vertex of a triangle to the middle point of side opposite to it. So there are three medians of a triangle.

Medians of any triangle are concurrent i.e. they all intersect at one point which is called centroid .

It can be proved that coordinates of the centroid of a triangle whose three vertices are (x_1,y_1),(x_2,y_2) and (x_3,y_3) are

((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)

For details see here.

As such coordinates of centroid of a triangle whose three vertices are (4,8),(2,-6) and (-4,4) are

((4+2-4)/3,(8-6+4)/3) or (2/3,2)