Let ABCD and A′B′C′D′ be two arbitrary parallelograms in the space, and let M, N, P, Q be points dividing the segments AA′, BB′, CC′, DD′ in equal ratios.
a.) Prove that the quadrilateral MNPQ is a parallelogram.
b.) What is the locus of the center of the parallelogram MNPQ, when the point M moves on the segment AA′ ?
(Consecutive vertices of the parallelograms are labelled in alphabetical order. geometryparallelogramvectorLocus problemsLocusIMO LonglistIMO Shortlist