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

**Solution:**

The slope of the line joining the origin (0, 0) and point (-2, 9), (9 - 0)/(- 2 - 0) = - 9/2

Accordingly, the slope of the line perpendicular to the line joining the origin and point (-2, 9) is the negative reciprocal of the above slope. i.e., - 1/(- 9/2) = 2/9

Now, the equation of the line passing through the point (-2, 9) and having a slope 2/9 is

(y - 9) = (2/9) (x + 2)

9y - 81 = 2x + 4

2x - 9y + 85 = 0

Thus, the equation of the line is 2x - 9y + 85 = 0

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.2 Question 15

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

**Summary:**

The equation of the line that is perpendicular from the origin to a line meets it at the point (-2, 9) is 2x - 9y + 85 = 0

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