A vertex of equilateral triangle is (2, 3) and equation of opposite side is x + y = 2, then equation

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9.Straight Line

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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

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

(IIT-1975)

Solution

(b) $y – 3 = \tan (\theta \pm {60^o})(x – 2)$

As $\theta = {135^o},$So $y – 3 = \frac{{ – 1 \pm \sqrt 3 }}{{1 \mp ( – \sqrt 3 )}}(x – 2)$

i.e., $y – 3 = \frac{{ – 1 + \sqrt 3 }}{{\sqrt 3 + 1}}(x – 2) = (2 – \sqrt 3 )(x – 2)$.

Standard 11

Mathematics

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