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. What are the vertices of the triangle?

Answer 1

"the midpoint of the base is at the origin" and "side 2a"

So, two vertices are at ( -a, 0 ) and ( a, 0 ).

The equilateral triangle is divided into two right triangles (aso the Pythagorean Theorem applies). Two sides are known: base = a and hypotenuse = 2a²

Using the Pythagorean theorem, the third side (on the y-axis is a√3.

(a²) + (a√3)² = (2a)²

a² + 3a² = 4a²

The third vertex is at ( 0, a√3 )

Answer 2

Draw and label a diagram!

(-a, 0), (0, a√3), (a, 0)