Question

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

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

Answer 1

Answer: (D)

$-\sqrt{3}$

Let the three points are $A(0,0)$ , $B($$3,\sqrt{3})$ and $C(3,\lambda )$

These are vertex of equilateral triangle then $AB=AC$

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

by squaring both side

$9+3=9+$${\lambda }^2$

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

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