SOLUTION: If you were given three points on a coordinate plane and asked to determine if they were connected they formed: a right triangle a scalene triangle an equilateral triangle

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right triangle--> if one angle measures 90 degrees or pi/2 radians. Moreover, the sides would follow the Pythagorean Formula: a^2+b^2=c^2, where a and b are sides opposite angles less than 90 degrees and c is the hypotenuse, the side opposite the right angle.
scalene triangle--> if all the sides are of different length and angles are of different measure.
equilateral triangle--> if all the sides are of the same length and all angles are of the same measure.

You would determine the length of sides using the distance formula

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if you are given with any three points with their coordinates then to prove that they form a right triangle you have to show that pythagoras theorem holds in it. if you show that all sides have different lengths using distance formula then it gives the proof of scalene triangle.if all sides are proved to be equal then it will be an equilateral triangle.hope this be helpful to you.