Question

Point 'p' lies on the line$ı\{(x,y)\mid 3x+5y=15\}$. if 'P' is also equidistant from the coordinate axis, then P can be located in which of the four quadrants

• A. I only
• B. II only
• C. I or II only
• D. IV only

Answer 1

The correct option is C I or II only

The line $3x+5y=15$ intersects the coordinate axis at $(5,0)$ and $(0,3)$ respectively.

For $P$ to be equidistant from the coordinate axis,

Case I:- $x=y$

$3x+5x=15$

$\Rightarrow x=\frac{15}{8}$

$\therefore y=x=\frac{15}{8}$.

Coordinates of $P$ will be $(\frac{15}{8},\frac{15}{8})\Rightarrow I$ quadrant.

Case II:- $y=-x$

$3x-5x=15$

$\Rightarrow x=-\frac{15}{2}$

$\therefore y=-x=\frac{15}{2}$.

Coordinates of $P$ will be $(-\frac{15}{2},\frac{15}{2})\Rightarrow II$ quadrant.

Hence for $P$ to be equidistant from the coordinate axis, it should lie in the first or second quadrant.