Question

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

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

Answer 1

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

From given, we have,

$A(0,0),B(3,\sqrt{3}),C(3,\lambda )$

Since the triangle is equilateral, we have

$A{B}^2=A{C}^2$

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

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

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