Home
Class 12
MATHS
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

0

B

4

C

9

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`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    CENGAGE|Exercise Comprehension Type|3 Videos

  • STRAIGHT LINE

    CENGAGE|Exercise Multiple Correct Answers Type|8 Videos

  • STATISTICS

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

Similar Questions

Explore conceptually related problems

If the centroid of the triangle ABC is at the origin and algebraic sum of the lengths of the perpendiculars from the vertices of the triangle ABC on the variable line L is equal to 1 then sum of the squares of the reciprocals of the intercepts made by L on the coordinate axes is equal to

The points A (x_(1),y_(1)), B (x_(2),y_(2)) and C (x_(3),y_(3)) are the vertices of Delta ABC . What are coordinate of the centroid of the triangle ABC ?

If A(1,a),B(a,a^(2)) and C(a^(2),a^(2)) are the vertices of a triangle which are equidistant from the origin,then the centroid of the triangle ABC is at the point

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 line L. If L intersects the sides BC,CA and AB of a triangle ABC at P,Q,R respectively, then (BP)/(PC)xx(CQ)/(QA)xx(AR)/(RB) is equal to

The algebraic sum of the perpendicular distances from the vertices of a triangle to a variable line is ‘O', then the line passes through the ------ of the triangle

If A(5,-1),B(-3,-2) and (-1,8) are the vertices of triangle ABC,find the length of median through A and the coordinates of the centroid.