Page 4 - LN

5m 1 + 5m 2 = 7m 1 + 2m 2
2m 1 = 3m 2

the required ratio is 3 : 2

Exa:5-Prove that the coordinates of the centroid of the ABC with vertices A(x 1 ,

y 1 ), B(x 2 , y 2 ) and C(x 3 , y 3 ) are

Let the vertices A, B and C of the triangle ABC be (x 1 , y 1 ), (x 2 , y 2 ) and (x 3 , y 3 ) respectively
and let D be the middle point of BC, as shown in figure.

Therefore,
Let G(x, y) be the centroid of the triangle.
We know that the point G divides AD in the ratio 2 : 1.
Therefore,

and
Exa:6-Find the centroid of the triangle ABC whose vertices are given as:
A(5, -1), B(-4, 3), C(-1, -2)
Soln:Centroid of a triangle whose vertices are (x1, y1), (x2, y2), (x3, y3) is

Centroid of ABC is

4