Question

Prove that the points A(2, 4), B(2, 6) and `C(2 + sqrt(3), 5)` are the vertices of an equilateral triangle.

Answer 1

The given points are A(2, 4), B(2, 6) and C(2 +`sqrt(3)`,5) Now 

`AB =sqrt(((2-2)^2 +(4-6)^2 )) = sqrt((0)^2 +(-2)^2)`

    `= sqrt((0+4) =2`

`BC = sqrt((2-2- sqrt(3))^2 + (6-5)^2 ) = sqrt((- sqrt(3))^2 +(1)^2)`

`= sqrt(3+1) = 2`

`AC = sqrt((2-2-sqrt(3))^2 + (4-5)^2 ) = sqrt((- sqrt(3))^2 +(-1)^2)`

`= sqrt(3+1) =2`

Hence, the points A(2, 4), B(2, 6) and C(2 +`sqrt(3)`,5) are the vertices of an equilateral triangle