Question

Abcd is a given parallelogram . What is the locus of remaining vertices of parallelogram equal in area

Answer 1

yes, to make sure just draw with horizontal AC,  mark origin in the mid.

If B and D are  at (x, y) & (−x, −y), the shape will be a parallelogram.

Area will be |AC|*|y|.

so that the  loci are horizontal lines that are just  parallel to AC.