Question

The vertices of a triangle are A(3, 4), B(2, 0), and C(−1, 6). Find the equation of the line containing the median AD

Answer 1

Since AD is the median, D is the midpoint of BC.

∴ D ≡ `((2 - 1)/2, (0 + 6)/2) = (1/2, 3)`

∴ median AD passes through the points A(3, 4) and `"D"(1/2, 3)`.

∴ equation of the median AD is

`(y - 4)/(x - 3) = (3 - 4)/(1/2 - 3)`

= `(-1)/((-5/2)`

= `2/5`

∴ 5y – 20 = 2x – 6

∴ 2x – 5y + 14 = 0.