Question

Show that the points A(1, 2), B(1, 6) and C(1+ 23, 4) are the vertices of an

equilateral triangle.​

Answer 1

Answer:

The Points A(1,2), B(1,6), C(1+2√3,4) are Vertices of an Equilateral Triangle.

Step-by-step explanation:

A = (1, 2)

B = (1 , 6)

C = (1 + 2√3) , 4)

Length of AB =$\sqrt{(1-1)^{2} +(6-2)^{2}$=$\sqrt{16}$=4

Length of AC =$\sqrt{(1+2\sqrt{3} -1)^{2} +(4-2)^{2}$=$\sqrt{16}$=4

Length of BC =$\sqrt{(1+2\sqrt{3} -1)^{2} +(4-6)^{2}$=$\sqrt{16}$=4

Length of AB = AC = BC = 4

It means Points A(1,2), B(1,6), C(1+2√3,4) are Vertices of an Equilateral Triangle.