Question

triangle ABC is a right isosceles triangle with hypotenuse AB. M is the midpoint of AB. Write a coordinate proof to show that Cm is perpendicular to AB

Answer 1

I'm assuming you use your own coordinates for them.
Use the midpoint formula on coordinate A and B to figure out M's coordinates, then to prove that CM is perpendicular to AB use slope formula
Midpoint formula: \[(\frac{ x_1 + x_2 }{ 2 }, \frac{ y_1 + y_2 }{ 2 })\]
Slope formula: \[(\frac{ y_2 - y_1}{ x_2 - x_1})\]