Q. 154.3( 80 Votes )

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

Answer :

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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