# Prove that the Points A(2, 4), B(2, 6) and (2 +Sqrt(3) ,5) Are the Vertices of an Equilateral Triangle - Mathematics

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

#### Solution

The given points are A(2, 4), b(2, 6) and (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 (2 +sqrt(3) ,5) are the vertices of an equilateral triangle

Concept: Area of a Triangle
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 22