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

Asked by Abhisek | 1 year ago |  122

##### Solution :-

Points are origin (0, 0) and (-2, 9).

We know that slope, m =

$$\dfrac{y_2+y_1}{x_2+x_1}$$

=$$\dfrac{9-0}{2-0}$$

$$- \dfrac{9}{2}$$

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 = ($$- \dfrac{1}{m}$$) = $$\dfrac{-1}{(-\dfrac{9}{2})}$$$$\dfrac{2}{9}$$

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 = ($$\dfrac{2}{9}$$) (x – (-2))

9(y – 9) = 2(x + 2)

9y – 81 = 2x + 4

2x + 4 – 9y + 81 = 0

2x – 9y + 85 = 0

The equation of line is 2x – 9y + 85 = 0.

Answered by Pragya Singh | 1 year ago

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