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If \mathrm{x^{2}-7 x y-y^{2}=0, x+y=2}, represents the sides of a triangle, then distance between orthocenter and the side of triangle is

Option: 1

2


Option: 2

\sqrt{ } 3


Option: 3

\sqrt{ } 2


Option: 4

\frac{1}{\sqrt{2 } }


Answers (1)

best_answer

Clearly \mathrm{x^2-7 x y+y^2=0} will represent two perpendicular lines \Rightarrow triangle will be a right angled triangle and ortho-centre will be the right angled vertex  which is (0, 0).

Clearly distance of (0,0) from \mathrm{x+y-2=0} is \mathrm{\sqrt{2}}.

Hence (C) is the correct answer.

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Ritika Harsh

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