# 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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