A Midpoint Locus of Skew Segments

★ 7/10plane geometry Parametrization solid geometry Symmetry

Problem

Points $A$ and $B$ lie on skew lines $a$ and $b$ respectively, and the segment $AB$ is perpendicular to both. Moving points $P\in a$ and $Q\in b$ satisfy that $PA+QB$ is constant. Determine the shape of the locus of the midpoint $M$ of the segment $PQ$ .

Answer

Solution

Difficulty	7/10
Topics	plane geometry, Parametrization, solid geometry, Symmetry

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.