`A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)` are the vertices of a triangle ABC. lx+my+n=0 is an equation of the line L.
Answer the following questions based on above passage :
If the centroid of the triangle ABC is at the origin and algebraic sum of the length of the perpendiculars from the vertices of the triangle ABC on the line L is equal to 1 then sum of the squares of the intercepts made by L on the coordinate axes is equal to

Options

A. (a) 0
B. (b) 4
C. (c) 9
D. (d) 16

Answer

C

Explanation

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`