Question

Prove that the co-ordinates of the a traingleABC
with vertisesA(X1,Y1),(X2,Y2)and(X3,Y3)are given b[X1+X2+X3/3,Y1+Y2+Y3/3]​

Answer 1

Answer:

Let A(x1,y1), B(x2,y2) and C(x3,y3) be the vertices of a triangle ABC whose medians are AD,BE and CF respectively. So, D,E and F are respectively the mid points of BC,CA and AB.

Coordinates of D are [(x3 + x2/2),(x3 + x2/2)]

Coordinates of a point G(x, y) dividing AD in the ratio 2 : 1 are

{[2(x2 + x3/2)+x1]/2+1 , [ 2(y2 + y3/2)+y1] 2+1}

(x1 + x2 + x3 / 3 , y1 + y2 + y3 / 3)

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