The perpendicular from the origin to a line meets it at the point (–2, 9), find the equation of the line.

Given points are origin (0, 0) and (-2, 9).

We know that slope, m =

We know that two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

∴ m = (-1/m) =

We know that the point (x, y) lies on the line with slope m through the fixed point (x₀, y₀), if and only if, its coordinates satisfy the equation y – y₀ = m (x – x₀)

∴ y – 9 = (2/9) (x – (-2))

⇒ 9(y – 9) = 2(x + 2)

⇒ 9y – 81 = 2x + 4

⇒ 2x + 4 – 9y + 81 = 0

⇒ 2x – 9y + 85 = 0

Ans. The equation of line is 2x – 9y + 85 = 0.