Question

A(8,5), B (-2,1) and C(5,4) are the vertices of a triangle. Find the equation of the median of the traingle through C.

Answer 1

Let CE be the median of ΔABC from C 

`therefore` AE : EB = 1 : 1

By using mid- point formula

Coordinates of E are,

E`((8 - 2)/2, (5 + 1)/2)` = E(3,3)

Equation of CE is `("y" - "y"_1)/("x" - "x"_1) = ("y"_2 - "y"_1)/("x"_2 -"x"_1)`

`("y" - 3)/("x" - 3) = (4 - 3)/(5 - 3)`

⇒ x - 3 = 2y - 6

⇒ x - 2y + 3 = 0

⇒ 2y + x + 3