- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Find the value of $a$ for which the following points $A( a,\ 3),\ B( 2,\ 1)$ and $C( 5,\ a)$ are collinear. Hence find the equation of the line.
Given: Points $A( a,\ 3),\ B( 2,\ 1)$ and $C( 5,\ a)$ are collinear.
To do: To find the value of $a$ and to find the equation of the line.
Solution:
As given, $A( a,\ 3),\ B( 2,\ 1)$ and $C( 5,\ a)$ are collinear.
$\therefore$ Slope of $AB=$ Slope of $BC$
$\Rightarrow \frac{1-3}{2-a}=\frac{a-1}{5-2}$
$\Rightarrow \frac{-2}{2-a}=\frac{a-1}{3}$
$\Rightarrow -6=( 2-a)( a-1)$
$\Rightarrow -6=2a-2-a^2+a$
$\Rightarrow a^2-3a-4=0$
$\Rightarrow a^2-4a+a-4=0$
$\Rightarrow ( a-4)( a+1)=0$
$a=4,\ -1$
For $a=4$
Slope of $BC=\frac{a-1}{5-2}=\frac{4-1}{3}=\frac{3}{3}=1$
Equation of $BC;\ ( y-1)=1( x-2)$
$\Rightarrow y-1=x-2$
$\Rightarrow x-y=1$
For $a=-1$
Slope of $BC=\frac{a-1}{5-2}$
$=\frac{-1-1}{3}$
$=-\frac{2}{3}$
Equation of $BC:( y-1)=-\frac{2}{3}( x-2)$
$\Rightarrow 3y-3=4-2x$
$\Rightarrow 2x+3y=7$
To Continue Learning Please Login
Login with Google