Question

A (4,2) B (6,8) C (8,4) are the vertices of triangle ABC. Write down the equation of the median of the triangle through A.

Answer 1

D is mid-point of BC

$D\equiv (\frac{6+8}{2},\frac{8+4}{2})$

$D(7,6)$

Equation of median through A

$=$Equation of AD

$\frac{6-2}{7-4}(x-4)=(y-2)$

$\Rightarrow 4(x-4)=3(y-2)$

$4x-16=3y-6$

$\Rightarrow 4x-3y=10$.