A person stands at the middle point of a wooden ladder which starts slipping between a vertical wall and the floor of a room, while continuing to remain in a vertical plane. The path traced by a person standing at the middle point of the slipping ladder is:

When a ladder of fixed length L has its ends on the floor and wall, the two ends and the corner form a right triangle; the midpoint of the ladder is the midpoint of the hypotenuse. The median to the hypotenuse of a right triangle equals half the hypotenuse, so the midpoint stays at a constant distance L/2 from the corner, tracing an arc of a circle centered at the corner as the ladder slides [1]. This is the well-known result that the locus of the midpoint is a circular arc (e.g., a 6‑ft ladder gives a radius 3 arc), and surveys and solutions state generally that the midpoint moves on a circle while other points trace ellipses.

Sources

1. [1] https://www.physics.harvard.edu/resource/sol47pdf