Question

The equation of a straight line passing through $(-3,2)$ and cutting an intercept equal in magnitude but opposite in signs from axes is given by:

• A. $x-y+5=0$
• B. $x+y-5=0$
• C. $x-y-5=0$
• D. $x+y+5=0$

Answer 1

The correct option is A

$x-y+5=0$

Determine the equation of the line :

Let the required line be $AB$

Given that: $AB$ passes through the point $(-3,2)$

Let the intercept on $x-axis$ be $a$ and $y-axis$ be $y$.

Therefore, the equation of $AB$ is:

$\begin{array}{rcl}\frac{x}{a}+\frac{y}{-a}& =& 1\\ & \Rightarrow & x-y=a\\ & & \end{array}$

Putting $x=-3,y=2$ in the above equation:

$\begin{array}{rcl}& \Rightarrow & -3-2=a\\ & \Rightarrow & a=-5\end{array}$

Substituting $a$ in the equation:

$\begin{array}{rcl}x-y& =& a\\ & \Rightarrow & x-y=-5\\ & \Rightarrow & x-y+5=0\end{array}$

Therefore, the equation of $AB$ is $x-y+5=0$.

Hence, the correct answer is Option (A).