If three points (0, 0),

Question:

If three points $(0,0),(3, \sqrt{3})$ and $(3, \lambda)$ form an equilateral triangle, then $\lambda=$

(a) 2

(b) −3

(c) −4

(d) None of these

Solution:

We have an equilateral triangle $\triangle \mathrm{ABC}$ whose co-ordinates are $\mathrm{A}(0,0) ; \mathrm{B}(3, \sqrt{3})$ and $\mathrm{C}(3, \lambda)$.

Since the triangle is equilateral. So,

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

So,

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

Cancel out the common terms from both the sides,

Therefore,

$\lambda=\sqrt{3}$