Q. 11 E3.8( 8 Votes )

If in triangle ABC, the co-ordinates of vertex A is (7, –4) and centroid of triangle is (1, 2), then the co-ordinates a mid point of BC is
A. (–2, –5)

B. (–2, 5)

C. (2, –5)

D. (5, –2)

Answer :

The ΔABC with coordinates of A as (7, -4) 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) = (7, -4) and


B = (x2, y2) and


C = (x3, y3)



G = (1, 2)


Centroid of a triangle is given by


G =


(1, 2) =


(1, 2) =


Equate x-coordinate and y-coordinate


= 1 and = 2


7 + x2 + x3 = 3 and – 4 + y2 + y3 = 6


x2 + x3 = -4 and y2 + y3 = 10


Divide by 2


= -2 and = 5


Thus midpoint M of BC is (-2, 5)

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