Question:
A point on the straight line, \(3x + 5y = 15\) which is equidistant from the coordinate axes will lie only in :
A point on the straight line, \(3x + 5y = 15\) which is equidistant from the coordinate axes will lie only in :
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Equidistant from the axes means \(|x| = |y|\), so the point lies on \(y = x\) or \(y = -x\); intersect each with the line.
Updated On: Nov 5, 2026
- 1st and 2nd qudratants
- 4th qudratant
- 1st and 2nd and 4th qudratants
- 1st qudratant
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The Correct Option is A
Solution and Explanation
Equidistant from the axes means \(|x| = |y|\), i.e. \(y = x\) or \(y = -x\).
With \(y = x\): \(3x + 5x = 15 \Rightarrow x = \frac{15}{8}\), the point \(\left(\frac{15}{8}, \frac{15}{8}\right)\) lies in the 1st quadrant.
With \(y = -x\): \(3x - 5x = 15 \Rightarrow x = -\frac{15}{2}\), \(y = \frac{15}{2}\), the point \(\left(-\frac{15}{2}, \frac{15}{2}\right)\) lies in the 2nd quadrant.
So such points lie only in the 1st and 2nd quadrants.
Answer: (1) 1st and 2nd qudratants
With \(y = x\): \(3x + 5x = 15 \Rightarrow x = \frac{15}{8}\), the point \(\left(\frac{15}{8}, \frac{15}{8}\right)\) lies in the 1st quadrant.
With \(y = -x\): \(3x - 5x = 15 \Rightarrow x = -\frac{15}{2}\), \(y = \frac{15}{2}\), the point \(\left(-\frac{15}{2}, \frac{15}{2}\right)\) lies in the 2nd quadrant.
So such points lie only in the 1st and 2nd quadrants.
Answer: (1) 1st and 2nd qudratants
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