Question

O(0, 0), A(3, 5) and B(−5, −3) are the vertices of triangle OAB. Find the equation of altitude of triangle OAB through vertex B.

Answer 1

The altitude through vertex B is perpendicular to OA.

Slope of OA = `(5 - 0)/( 3 - 0) = 5/3`

Slope of the required altitude = `(-1)/(5/3)= (-3)/5`

The equation of the required altitude through B is

y – y₁ = m(x – x₁)

`y + 3 = (-3)/5 (x + 5)`

5y + 15 = −3x − 15

3x + 5y + 30 = 0