Straight Lines
Points Equidistant from Axes
JEE Main 2019
Grade 11
Question:
A point on the line $3x + 5y = 15$ which is equidistant from the coordinate axes lies only in the quadrant(s):
(1) $1^{\text{st}}$ only
(2) $1^{\text{st}}$ and $2^{\text{nd}}$
(3) $1^{\text{st}}$ and $4^{\text{th}}$
(4) $2^{\text{nd}}$ and $4^{\text{th}}$
Step-by-Step Solution
Key Concept: Equidistant from axes means $|x| = |y|$, i.e., $y = x$ or $y = -x$. Substitute each case into $3x + 5y = 15$ and determine the sign of the coordinates.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)