The coordinates of two vertices of an equilateral triangle are (-6,0) and (6,0). What is the third vertex?

Question

Choices are: 

A. (0,3sqrt3)

B. (6,6sqrt3)

C. (0,6sqrt3)

D. (0,6)

Answer 1

the two vertices given are on the x-axis

the distance between them is 12 units (-6 to 6 is 12 units)

using quadrant 1, form a right triangle with the positive part of the x-axis and the positive part of the y-axis being the legs of the right triangle

the hypotenuse must be 12 units because we have an equilateral triangle

using the Pythagorean Theorem...

12²=6²+y² where y is the distance to the third vertex and therefore the y-coordinate of the third vertex

144=36+y²

144-36=y²

108=y²

y²=108

y=√108

y=√36*3

y=6√3

the third vertex is (0, 6√3) which is C.