Question

Prove that the points (0,3) , (4,3) and `(2, 3+2sqrt 3)` are the vertices of an equilateral triangle.

Answer 1

AB = `sqrt ((0 - 4)^2 + (3 - 3)^2)` = 4 units

BC = `sqrt ((4 - 2)^2 + (3 - 3 - 2sqrt 3)^2) = sqrt (4 + 12)` = 4 units

AC = `sqrt ((2 - 0)^2 + (3 + 2 sqrt 3 - 3)^2) = sqrt (4 + 12) ` = 4 units

∵ AB = BC = AC

∴ ABC is an equilateral triangle.