Question 756615
Q:
prove that the three points A(-5,0) B(3,0) and C(-1, 4&#8730;3) are the vertices of an equilateral triangle
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A:
Using distance formula:
AB = {{{sqrt((0 - 0)^2 + (3 - (-5))^2)}}} = 8
AC = {{{sqrt((4sqrt(3) - 0)^2 + (-1 - (-5))^2)}}} = 8
BC = {{{sqrt((4sqrt(3) - 0)^2 + (-1 - 3)^2)}}} = 8
All three sides are equal, therefore A, B, and C are the vertices of an equilateral triangle. &#9632;