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 a line:

y – y₁ = `(y_2 - y_1)/(x_2 - x_1) (x - x_1)`

Substituting values, we get:

Equation of AD:

⇒ y – (–1) = `(4 - (-1))/(-3 - 1) (x - 1)`

⇒ y + 1 = `5/-4 (x - 1)`

⇒ –4(y + 1) = 5(x – 1)

⇒ –4y – 4 = 5x – 5

⇒ 5x + 4y = –4 + 5

⇒ 5x + 4y = 1

Hence, equation of median AD is 5x + 4y = 1