prove that the points (0,0) ,(5,5) and (-5,5) are the vertices of a right isosceles 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