Q. 154.4( 75 Votes )
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.
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