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

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1 Answer

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.