prove that the points (0,0), (5,5), (-5,5) are the vertices of a right angled triangle.

Let the vertices be A(0,0); B(5,5) and C(-5,5).Remember that in a right triangle Pythagoras theorem will be followed.Also for an isosceles triangle two sides must be of the same length.By distance formula: The triangle is clearly isosceles as AB = AC.
Also,AB² + AC² = 50 + 50 = 100 = 10² = BC²
​So, by converse of pythagoras theorem, , given triangle is a right triangle in which, angle A is 90⁰