Question

Given the line $3x+5y=15$ and a point on this line equidistant from the coordinate axes. Such a point exists in:

• A. None of the quadrants
• B. Quadrant I only
• C. Quadrant I, II only
• D. Quadrants I, II, III only
• E. Each of the quadrants

Answer 1

The correct option is C Quadrant I, II only

The locus of points equidistant from the coordinate axes is the pair of lines $y=x$ and $y=-x$.
Solve simultaneously $3x+5y=15$ and $y=x$ to obtain $x=y=\frac{15}{8}.$The point $(\frac{15}{8},\frac{15}{8})$in quadrant I, therefore satisfies the required condition. Solve simultaneously $3x+5y=15$ and $y=-x$ to obtain $x=-\frac{15}{2},y=\frac{15}{2}.$ The point $(-\frac{15}{2},\frac{15}{2})$ in quadrant II, therefore satisfies the required conditions.
There are no other solutions to these pairs of equations, and, therefore, no other points satisfying the required condition.