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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.
Solution
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
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