Question

The vertices of a triangle ABC are $A(-3,4),B(6,-2)andC(2,5)$. Find the equation of the median passing through the point A.

Answer 1

$A(-3,4)B(6,-2)C(2,5)$

equation of median passing through $A$

mid point of $BC\Rightarrow (\frac{6+2}{2},\frac{-2+5}{2})$

$\Rightarrow (4,\frac{3}{2})$

$\therefore$ equation of median $=$ line passing through $(-3,4)$ and $(4,\frac{3}{2})$

$(y-4)=\frac{(4-\frac{3}{2})}{(-3-4)}\times (x+3)$

$\Rightarrow (y-4)=\frac{-5}{14}(x+3)$

$\Rightarrow 14y-56=-5x-15$

$\Rightarrow 14y+5x=41$