Question

ABC is a triangle whose vertices are A(1, –1), B(0, 4) and C(– 6, 4). D is the midpoint of BC. Find the equation of the median AD.

Answer 1

Equation of median AD

y – y₁ = ${\displaystyle \frac{y_2-y_1}{x_2-x_1}(x-x_1)}$

${\displaystyle \Rightarrow }$ y – (–1) = ${\displaystyle \frac{4-(-1)}{-3-1}(x-1)}$

${\displaystyle \Rightarrow }$ y + 1 = ${\displaystyle \frac{5}{-4}(x-1)}$

${\displaystyle \Rightarrow }$ – 4y – 4 = 5x – 5

i.e. 5x + 4y = 1