Question

Show that the points A(1,2), B(1,6), C(1+2√3,4) are vertices of an equilateral triangle.

Answer 1

Hope it helps............

Answer 2

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 = $\sqrt{(1-1)^2 + (6-2)^2} = \sqrt{0^2 + 4^2} = \sqrt{0 + 16} = \sqrt{16} = 4$

Length of AC = $\sqrt{(1+2\sqrt{3}-1)^2 + (4-2)^2} = \sqrt{(2\sqrt{3})^2 + 2^2} = \sqrt{12 + 4} = \sqrt{16} = 4$

Length of BC = $\sqrt{(1+2\sqrt{3}-1)^2 + (4-6)^2} = \sqrt{(2\sqrt{3})^2 + (-2)^2} = \sqrt{12 + 4} = \sqrt{16} = 4$

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.