Straight LineHardBloom L3
Question
Drawn from the origin are two mutually perpendicular straight lines forming an isosceles together with the straight line, $2x + y = a$. Then the area of triangle is :
Options
A.$\frac{a^{2}}{2}$
B.$\frac{a^{2}}{3}$
C.$\frac{a^{2}}{5}$
D.None
Solution
Sol. [Key Concept: Two mutually perpendicular lines from $O$ with a fixed line form an isosceles right triangle; with foot-distance $p$, area $= \frac{1}{2}(2p)(p) = p^{2}$.]
$$OD = AD = BD $$
$$OD = P = \frac{|a|}{\sqrt{5}} $$Area of $\bigtriangleup OAB = \frac{1}{2}(2P)P = P^{2}$
Area $= \frac{a^{2}}{5}$
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