Question

A point on the straight line, $3x + 5y = 15$ which is equidistant from the coordinate axes will lie only in:

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

Answer 1

Answer: (A)

Now, $\left| \frac{15-3t}{5}\right| = \left|t\right| $
$ \Rightarrow \frac{15-3t}{5} =t$ or $\frac{15-3t}{5} =-t $
$ \therefore t = \frac{15}{8} $ or $ t = \frac{-15}{2} $
So, $ P\left(\frac{15}{8} , \frac{15}{8}\right) \in I^{st} $ quadrant
or $ P\left(\frac{-15}{2}, \frac{15}{2}\right)\in II^{nd } $ quadrant