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Question
Answer the following question:
The perpendicular from the origin to a line meets it at (−2, 9). Find the equation of the line.
Solution
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
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