Question
The perpendicular from the origin to a line meets it at the point (-2, 9), find the equation of the line.
✓
Answer
Slope of line $OP = \frac{{9 - 0}}{{ - 2 - 0}} = \frac{{ - 9}}{2}$
Since the required line is perpendicular to OP,
$\therefore$ Slope of required line $ = \frac{2}{9}$
The required line passing through point (-2, 9) having slope $\frac{2}{9}$.
So equation of required line is
$y - 9 = \frac{2}{9}(x + 2) \Rightarrow$ 9y - 81 = 2 x + 4
$\Rightarrow$ 2x - 9y + 85 = 0
Since the required line is perpendicular to OP,
$\therefore$ Slope of required line $ = \frac{2}{9}$
The required line passing through point (-2, 9) having slope $\frac{2}{9}$.
So equation of required line is
$y - 9 = \frac{2}{9}(x + 2) \Rightarrow$ 9y - 81 = 2 x + 4
$\Rightarrow$ 2x - 9y + 85 = 0
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