If three points (0,0), (3, √3) and (3, λ) form an equilateral triangle . . .

Question : If three points (0,0), (3, √3) and (3, λ) form an equilateral triangle, then λ equals 

a) 2

b) -3

c) -4

d) None of These.

Doubt by Gauri

Solution : 

Let
A (0,0)

B (3, √3)

C (3, λ) 

ABC is an equilateral triangle (Given)
Therefore, AB=BC=AC

AB = AC

√[(3-0)²+(√3-0)²] = √[(3-0)²+(λ-0)²]

[∵ Using Distance Formula]

Squaring both sides

(3-0)²+(√3-0)² = (3-0)²+(λ-0)²
(3)² + (√3)² = (3)²+λ²
9 + 3 = 9 + λ²
9+3-9 = λ²
3 = λ²
λ = ±√3
λ = √3 or -√3

Hence, c) would be the correct option.