Question

In triangle ABC, A (o,o) , <BAC = 30 degree , AC =2 and midpoint of segment AB is (4,0) and if B is on the x axis, find the centroid of triangle ABC

Answer 1

The line drawn from each vertex of a
triangle to the midpoint of the opposite side will intersect at the center of the triangle. The point of
intersection is called the Centroid.

A(0,0),B(8,0),C(Xc,Yc).

Xc = 2cos30 = 1.732.
Yc = 2sin30 = 1.

A(0,0),B(8,0),C(1.73,1).

Xo = (Xa + Xb + Xc) / 3,
Xo = (0 + 8 + 1.73) / 3 = 3.24.

Yo = (Ya + yB + Yc) / 3,
Yo = (0 + 0 + 1) / 3 = 1/3 = 0.3333.

Co-ordinates of the Centroid:
C(Xo,Yo),
C(3.24,0.333).