Q. 84.2( 16 Votes )

# 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.

Answer :

The ΔABC with coordinates of A as (2, 5) and assuming B and C coordinates to be (x_{2}, y_{2}) and (x_{3}, y_{3}) 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 = (x_{1}, y_{1}) = (2, 5) and

B = (x_{2}, y_{2}) and

C = (x_{3}, y_{3})

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 + x_{2} + x_{3} = -6 and 5 + y_{2} + y_{3} = 3

⇒ x_{2} + x_{3} = -8 and y_{2} + y_{3} = -2

Divide by 2

⇒ = -4 and = -1

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

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