Question

In a triangle ABC, co-ordinates of A are (1,2) and the equations of the medians through B and C are x + y = 5 and x = 4 respectively. Then the coordinates of B and C will be

Answer 1

ΔABC has vertex A(1,2)

Given that midpoint of AC is D and mid point of AB is E

Also,

Equation of medium BD is x + y = 5

Equation of medium CE is x = 4

Let coordinate of B(p, q) and C(r, s)

And point B(p, q) lies on the line BD [x + y  =4]

∴ p + q = 4

⇒ q = −3

∴ B ≡ (7, −3)

Point C(r, s) lies on CE  [x = 4]

∴ r = 4

∴ Coordinates of B & C are (7,−3) & (4,3).