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,

AB^{2} + AC^{2} = 50 + 50 = 100 = 10^{2} = BC^{2}

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