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Find the perpendicular distance of point (2, 4) from line 2x+y-5=0.(a) \(\frac{6}{\sqrt{5}}\)(b) \(\frac{3}{\sqrt{5}}\)(c) \(\frac{9}{\sqrt{5}}\)(d) \(\frac{3}{\sqrt{2}}\)I got this question during an interview for a job.Question is from Distance of a Point from a Line topic in chapter Straight Lines of Mathematics – Class 11

Answer»

Right answer is (b) \(\frac{3}{\SQRT{5}}\)

For EXPLANATION: Distance of point (x1, y1) from LINE ax +by +c=0 is \(|\frac{ax1+by1+c}{\sqrt{a^2+b^2}}|\).

So, distance of point (2, 4) from line 2x+y-5=0 is \(|\frac{2*2+4*1-5}{\sqrt{2^2+1^2}}| = \frac{3}{\sqrt{5}}\).


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