Section Formulas

Internal division: Division of line segment PQ internally.

The coordinates of a point R that divides line segment PQ with coordinates P(x1,y1,z1) and Q(x2,y2,z2) in the ratio m1:m2 internally are



[ (m1x2+m2x1)/(m1+m2), (m1y2+m2y1)/(m1+m2), (m1z2+m2z1)/(m1+m2)]


PR:RQ = m1:m2

If the is the mid point that m1:m2 = 1:1 the coordinates are
[(x1+x2)/2, (y1+y2)/2, (z1+z2)/2]

External division: Division of line segment PQ internally.

The coordinates of a point R that divides line segment PQ with coordinates P(x1,y1,z1) and Q(x2,y2,z2) in the ratio m1:m2 externally are

[ (m1x2 -m2x1)/(m1+m2), (m1y2 -m2y1)/(m1+m2), (m1z2 -m2z1)/(m1+m2)]

PR:RQ = m1:m2