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?

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Answer 1 · 2017-11-16T15:21:26

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

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)#

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)#