Straight Line Question 378

Question: A vertex of equilateral triangle is (2, 3) and equation of opposite side is $ x+y=2, $ then the equation of one side from rest two, is [IIT 1975]

Options:

A) $ y-3=2(x-2) $

B) $ y-3=(2-\sqrt{3})(x-2) $

C) $ y-3=(\sqrt{3}-1)(x-2) $

D)None of these

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ y-3=\tan (\theta \pm 60^{o})(x-2) $ As $ \theta =135^{o}, $ So $ y-3=\frac{-1\pm \sqrt{3}}{1\mp (-\sqrt{3})}(x-2) $ i.e., $ y-3=\frac{-1+\sqrt{3}}{\sqrt{3}+1}(x-2)=(2-\sqrt{3})(x-2) $ .