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

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)