HINT.-In your five figures angle $\angle{AED}$ is right so in your last figure, points $K,E,D$ (whose coordinates are known) determine a circle whose diameter is $\overline{KD}$. One way to finish is to verify that point $M$ belongs to this circle which is easy to do.

HINT.-In your five figures angle $\angle{KED}$ is right so in your last figure, points $K,E,D$ (whose coordinates are known) determine a circle whose diameter is $\overline{KD}$. One way to finish is to verify that point $M$ belongs to this circle which is easy to do.