Question

I am given the coordinates of three points and am asked to determine if they form an isosceles triangle how would i do this?

Answer 1

Take the distances between all three points. If two are equivalent, they are isosceles.

Answer 2

In general:
$$A(x_0, y_0) \\ B(x_1, y_1) \\ C(x_2, y_2) \\
s_0 = \sqrt{(x_1 - x_0)^2 + (y_1 - y_0)^2} \\
s_1 = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} \\
s_2 = \sqrt{(x_2 - x_0)^2 + (y_2 - y_0)^2}
$$
If \(s_x\) for any \(x \in \{0, 1, 2\}\) have two equivalencies, it is isosceles.

Answer 3

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