triangle

Name the points as say A,B and C.

 Find distances AB,BC,CA using the distance formula.

 Then, check the following.

AB+BC>AC

BC+CA>AB

CA+AB>BC

This property that the sum of any two sides of a triangle is always greater than the third side  must be satisfied for any 3 line segments to be the sides of a triangle.

 If the property is not satisfied, then the re can't be a triangle with these points as vertices.

Depending on the lengths of the sides you can conclude whether the given triangle is equilateral, isoceles or scelene using definitions of these terms.