Question

The base of an equilateral triangle with side 2A lies along the y-axis such that the midpoint of the base is at the origin find the vertices if the triangle

Answer 1

∆ABC is an equilateral, then AB = BC

AB² = BC²

use distance formula,

distance between (x₁,y₁) and (x₁,y₂) = √{(x₂-x₁)² +(y₂-y₁)²}

( h - 0 )² + ( 0 - a )² = (2a)²

h² + a² = 4a²

h² = 3a²

h = ±√3a

hence, the vertices of traingle are ( √3a, 0) , (0,a) and ( 0, -a) .