Question

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 1

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 \(|\frac{2*2+4*1-5}{\sqrt{2^2+1^2}}| = \frac{3}{\sqrt{5}}\).