Question

Answer the following question:

The perpendicular from the origin to a line meets it at (−2, 9). Find the equation of the line.

Answer 1

Slope of ON = `(9 - 0)/(-2 - 0) = (-9)/2`

Since line AB ⊥ ON,

slope of the line AB perpendicular to ON is `2/9`

and it passes through point N(–2, 9).

Equation of the line in slope point form is

y – y₁ = m(x – x₁)

∴ Equation of line AB is

y – 9 = `2/9(x + 2)`

∴ 9(y – 9) = 2(x + 2)

∴ 9y – 81 = 2x + 4

∴ 2x – 9y + 85 = 0