Q. An equilateral $\mathrm{\Delta}\ ABC$ in first quadrant is such that $A$ lies on $x$-axis, $B$ lies on $y$-axis and $BC$ is parallel to $x$-axis, then equation of straight line through $C$ parallel to $AB$ is (‘$a$’ is length of the side)
A) $y - \sqrt{3}x = \frac{3a\sqrt{3}}{2}$
B) $\sqrt{3}y + x = \frac{3a\sqrt{3}}{2}$
C) $y + \sqrt{3}x = \frac{3a\sqrt{3}}{2}$
D) None of these
Explanation
(c)
$y - \frac{a\sqrt{3}}{2} = \left( - \sqrt{3} \right)(x - a)$
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$\Rightarrow \ y - \frac{a\sqrt{3}}{2} = - \sqrt{3}x + a\sqrt{3}$
$\Rightarrow \ y + \sqrt{3}x = \frac{3a\sqrt{3}}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.