Q8 of 23 Page 330

In triangle ABC, co-ordinate of A is (2, 5) and the centroid of triangle is (–2, 1), let us find the co-ordinate of mid point of BC.

The ΔABC with coordinates of A as (2, 5) and assuming B and C coordinates to be (x2, y2) and (x3, y3) respectively as shown


M is the midpoint of segment BC with coordinates as shown and G is the centroid


The vertices of ΔABC with their coordinates are


A = (x1, y1) = (2, 5) and


B = (x2, y2) and


C = (x3, y3)



G = (-2, 1)


Centroid of a triangle is given by


G =


⇒ (-2, 1) =


⇒ (-2, 1) =


Equate x-coordinate and y-coordinate


⇒ = -2 and = 1


⇒ 2 + x2 + x3 = -6 and 5 + y2 + y3 = 3


⇒ x2 + x3 = -8 and y2 + y3 = -2


Divide by 2


⇒ = -4 and = -1


Thus midpoint M of BC is (-4, -1)


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