Find the perpendicular distance of the point (5,−3) from the line 2x+3y=6.

Step-by-step solution

1. Compute the numerator: $|2\times 5+3\times (-3)-6|=|10-9-6|=|-5|=5$.
2. Compute the denominator: $\sqrt{2^2+3^2}=\sqrt{4+9}=\sqrt{13}$.
3. Divide the numerator by the denominator: $5/\sqrt{13}$.
4. Thus the perpendicular distance is $5/\sqrt{13}$.

Concept tested: Distance from point to line

Published 16 October 2026 · How this solution was prepared and checked