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A(x1, y1), B(x2,y2), C(x3,y3) are three ...

`A(x_1, y_1), B(x_2,y_2), C(x_3,y_3)` are three vertices of a triangle ABC. `lx+my+n=0` is an equation of the line L. If the centroid of the triangle ABC is at the origin and algebraic sum of the lengths of the perpendicular from O the vertices of triangle ABC on the line L is equal to, then sum of the squares of reciprocals of the intercepts made by L on the coordinate axes is equal to

A

(a) 0

B

(b) 4

C

(c) 9

D

(d) 16

Text Solution

Verified by Experts

The correct Answer is:
C
Centroid is `G(0,0)`
`rArr x_(1) +x_(2) +x_(3) = y_(1)+y_(2) +y_(3) =0`
Given `sum ((lx_(1)+my_(1)+n))/(sqrt(l^(2)+m^(2))) =1`
`rArrl^(2) +m^(2) = 9n^(2)`
`rArr (l^(2)+m^(2))/(n^(2)) =9`
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