On a quadrilateral construct exterior squares on its sides.Then the lines connecting the centers of squares on opposite sides are congruent and perpendicular.

Drag B (segment AB will be dragged).

Compare the velocities of points X, K, and T.

DA is sqrt 2 DK rotated 45^o. CB is sqrt 2 CT rotated 45^o the other way. The velocity of segment AB (which is the same as the velocity of point X) is sqrt 2 the velocity of K rotated 45^o, and equal to sqrt 2 the velocity of T rotated 45^o the other way. Therefore PX = KT rotated 90^o plus a constant. To see that the constant is zero, make A coincide with D.