Question

show that the point P(2,3),Q(2,5),R(2+√3,4)are the vertices of an equilateral triangle.​

Answer 1

Step-by-step explanation:

let A(2,3) B(2,5) C(2+√3,4)

AB=√(2-2)^2+(5-3)^2=√0+4=2

BC=√(2+√3-2)^2+(4-5)^2=√(√3)^2+1=2

CA=√(2-2-√3)^2+(3-4)^2=√3+1=2

THUS

AB=BC=CA

SO THIS IS, AN EQUILATERAL TRIANGLE