(C) Let the points be $A\left( 0, \frac{8}{3} \right)$,$B(1, 3)$,and $C(82, 30)$.Slope of $AB = \frac{3 - \frac{8}{3}}{1 - 0} = \frac{\frac{9-8}{3}}{1

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) Let the points be $A\left( 0, \frac{8}{3} \right)$,$B(1, 3)$,and $C(82, 30)$.Slope of $AB = \frac{3 - \frac{8}{3}}{1 - 0} = \frac{\frac{9-8}{3}}{1} = \frac{1}{3}$.Slope of $BC = \frac{30 - 3}{82 - 1} = \frac{27}{81} = \frac{1}{3}$.Since the slope of $AB$ is equal to the slope of $BC$ and they share a common point $B$,the points $A$,$B$,and $C$ are collinear,meaning they lie on a straight line.

Class 11 Mathematics Straight Lines Concurrency of three lines

Difficult

The points $\left( 0, \frac{8}{3} \right)$,$(1, 3)$,and $(82, 30)$

JEE MAIN 2015 All JEE MAIN

A
form an acute angled triangle.
B
form a right angled triangle.
C
lie on a straight line.
D
form an obtuse angled triangle.

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Straight Lines

Subtopic

Concurrency of three lines

Previous Year

JEE MAIN 2015 Paper All JEE MAIN years →

If the three distinct lines $x + 2ay + a = 0$,$x + 3by + b = 0$,and $x + 4ay + a = 0$ are concurrent,then the point $(a, b)$ lies on a

DifficultJEE MAIN 2014

View Solution

If the lines $2x + y - 3 = 0$,$3x + 2y - 2 = 0$,and $kx - 3y - 23 = 0$ are concurrent,then the roots of the equation $6x^2 - 7x + k = 0$ are

EasyAP EAMCET 2017

View Solution

The lines $ax + by + c = 0$,where $3a + 2b + 4c = 0$,are concurrent at the point:

MediumIIT 1982

View Solution

Find the equation of a line passing through the point of intersection of the lines $2x - 3y + 4 = 0$ and $3x + 4y - 5 = 0$ and perpendicular to the line $6x - 7y + 3 = 0$.

Easy

View Solution

If the straight lines $ax + amy + 1 = 0$,$bx + (m + 1)by + 1 = 0$,and $cx + (m + 2)cy + 1 = 0$ $(m \neq 0)$ are concurrent,then $a, b, c$ are in:

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The points $\left( 0, \frac{8}{3} \right)$,$(1, 3)$,and $(82, 30)$

Similar Questions

If the three distinct lines $x + 2ay + a = 0$,$x + 3by + b = 0$,and $x + 4ay + a = 0$ are concurrent,then the point $(a, b)$ lies on a

If the lines $2x + y - 3 = 0$,$3x + 2y - 2 = 0$,and $kx - 3y - 23 = 0$ are concurrent,then the roots of the equation $6x^2 - 7x + k = 0$ are

The lines $ax + by + c = 0$,where $3a + 2b + 4c = 0$,are concurrent at the point:

Find the equation of a line passing through the point of intersection of the lines $2x - 3y + 4 = 0$ and $3x + 4y - 5 = 0$ and perpendicular to the line $6x - 7y + 3 = 0$.

If the straight lines $ax + amy + 1 = 0$,$bx + (m + 1)by + 1 = 0$,and $cx + (m + 2)cy + 1 = 0$ $(m \neq 0)$ are concurrent,then $a, b, c$ are in:

Vedclass Test Series

Exam Paper Generator

Online Exam Module