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: -Maths 9th

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: -Maths 9th
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Answer :

(b) \(rac{\sqrt{17}}{2}\)Equation of the line through the points (5, 0) and (0, 3) y – 0 = \(rac{3-0}{0-5}\) (x - 5)⇒ y = \(rac{-3}{5}\)(x - 5)⇒ 5y + 3x – 15 = 0 ∴ Distance of perpendicular from point (4, 4) on the line 5y + 3x – 15 = 0 is \(\bigg|rac{5 imes4+3 imes4-15}{\sqrt{5^2+3^2}}\bigg|\)= \(rac{|20+12-15|}{\sqrt{25+9}{}}\) = \(rac{17}{\sqrt{34}}\) units. = \(rac{\sqrt{17}}{2}\) units.
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