Midpoints

Corollary concerning midpoints and endpoints of chords A corollary of the above discussion is that if a parabola has several parallel chords, their midpoints all lie on a line which is parallel to the axis of symmetry.

A line segment joining a vertex of a tetrahedron with the centroid of the opposite face is called a median and a line segment joining the midpoints of two opposite edges is called a bimedian of the tetrahedron.

All non-self-crossing quadrilaterals tile the plane by repeated rotation around the midpoints of their edges.

At the midpoints between these four solar events, cross-quarter days are celebrated.

He secured the feathers at their midpoints with string and at their bases with wax, and gave the whole a gentle curvature like the wings of a bird.

The intervals above all have the same length on them, with the "midpoints" actually midway.

These are the distances from the center of the polyhedron to the vertices, edge midpoints, and face centers respectively.

The two bimedians in a quadrilateral and the line segment joining the midpoints of the diagonals in that quadrilateral are concurrent and are all bisected by their point of intersection.

The vertices of the octahedron lie at the midpoints of the edges of the tetrahedron, and in this sense it relates to the tetrahedron in the same way that the cuboctahedron and icosidodecahedron relate to the other Platonic solids.

Three of them are the medians of the triangle (which connect the sides' midpoints with the opposite vertices), and these are concurrent at the triangle's centroid ; indeed, they are the only area bisectors that go through the centroid.

Thus : where x is the distance between the midpoints of the diagonals.