Question

A Point On The Straight Line $3x+5y=15$ Which Is Equidistant From The Coordinate Axes Will Lie Only In

• A. $1^{st},2^{nd}$ and $4^{th}$quadrants
• B. $1^{st}$ and $2^{nd}$quadrants
• C. $4^{th}$quadrant
• D. $1^{st}$quadrant

Answer 1

The correct option is B

$1^{st}$ and $2^{nd}$quadrants

Explanation for the correct option:

Step 1: Put $x=y$ in the equation of the line.

As the point is equidistant from both the axes.

So, it should have equal ordinates.

$\begin{array}{rcl}3x+5x& =& 15\end{array}$

$\Rightarrow$ $\begin{array}{rcl}8x& =& 15\end{array}$

$\Rightarrow$ $\begin{array}{rcl}x& =& \frac{15}{8}\end{array}$

So, $y=\frac{15}{8}$

Note that $\left(\frac{15}{8},\frac{15}{8}\right)$ lies in $1^{st}$ quadrant.

Step 2: Put $x=-y$ in the equation of the line.

As the point is equidistant from both the axes.

So, it should have equal ordinates.

$\begin{array}{rcl}3x-5x& =& 15\end{array}$

$\Rightarrow$ $\begin{array}{rcl}-2x& =& 15\end{array}$

$\Rightarrow$ $\begin{array}{rcl}x& =& -\frac{15}{2}\end{array}$

So, $y=\frac{15}{2}$

Note that $\left(-\frac{15}{2},\frac{15}{2}\right)$ lies in $2^{nd}$ quadrant.

Hence, option (B) is the correct answer.