Question

Three points $\left(0,0\right),\left(3,\sqrt{3}\right),\left(3,\lambda \right)$ from an equilateral triangle, then $\lambda$ is equal to

• A. $2$
• B. $-3$
• C. $-4$
• D. $-\sqrt{3}$

Answer 1

The correct option is D $-\sqrt{3}$

Given:An equilateral triangle $ABC$ whose coordinates are $A(0,0),B(3,\sqrt{3})$ and $C(3,\lambda )$

Since the triangle is equilateral, we have

${AB}^2={AC}^2$

So,${(3-0)}^2+{(\sqrt{3}-0)}^2={(3-0)}^2+{(\lambda -0)}^2$

$\Rightarrow {(\sqrt{3}-0)}^2={(\lambda -0)}^2$

$\Rightarrow {\lambda }^2=3$

$\therefore \lambda =\pm \sqrt{3}$