If p be the length of the perpendicular from the origin on the straight line ax + by = p and b -Maths 9th

If p be the length of the perpendicular from the origin on the straight line ax + by = p and b -Maths 9th
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Answer :

(d) \(rac{17}{\sqrt{13}};\) 17 sq. unitsEquation of line BC : y – 7 = \(rac{1-7}{5-1}(x-1)\)⇒ y – 7 = \(rac{-6}{4}(x-1)\)⇒ 2 (y – 7) = –3 (x – 1) ⇒ 2y – 14 = –3x + 3 ⇒ 3x + 2y – 17 = 0. ∴ Distance of perpendicular from A(0, 0) on BC ≡ 3x + 2y – 11 = 0 is \(rac{|3 imes0+2 imes0-17|}{\sqrt{3^2+2^2}}\) = \(rac{17}{\sqrt{13}}\)Area of ΔABC = \(rac{1}{2}\) x BC x perpendicular distanceBC = \(\sqrt{(5-1)^2+(1-7)^2}\) = \(\sqrt{4^2+6^2}{}\) = \(\sqrt{16+36}\)= \(\sqrt{52}\) = \(2\sqrt{13}\)∴ Required area = \(rac{1}{2}\) x \(rac{17}{\sqrt{13}}\) x \(2\sqrt{13}\) = 17 sq. units.
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