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.

• 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

Answer 1

Answer: (B)

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

Answer 2

$y - 3 = \tan \left( \theta \pm 60 ^ { \circ } \right) ( x - 2 )$

As So $y - 3 = \frac { - 1 \pm \sqrt { 3 } } { 1 \mp ( - \sqrt { 3 } ) } ( x - 2 )$

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