Question

A straight line passes through the points (5, 0) and (0, 3). The length of the perpendicular from the point (4, 4) on the line is:

(a) \(\frac{\sqrt{17}}{2}\)

(b) \(\frac{\sqrt{17}}{2}\)

(c) \(\frac{15}{\sqrt{34}}\)

(d) \(\frac{17}{2}\)

Answer 1

(b) \(\frac{\sqrt{17}}{2}\)

Equation of the line through the points (5, 0) and (0, 3) 

y – 0 = \(\frac{3-0}{0-5}\) (x - 5)

⇒ y = \(\frac{-3}{5}\)(x - 5)

⇒ 5y + 3x – 15 = 0 

∴ Distance of perpendicular from point (4, 4) on the line

 5y + 3x – 15 = 0 is \(\bigg|\frac{5\times4+3\times4-15}{\sqrt{5^2+3^2}}\bigg|\)

= \(\frac{|20+12-15|}{\sqrt{25+9}{}}\) = \(\frac{17}{\sqrt{34}}\) units. = \(\frac{\sqrt{17}}{2}\) units.