## Quick Reference

Let *A* and *B* be points in the plane with Cartesian coordinates (*x*_{1}, *y*_{1}) and (*x*_{2}, *y*_{2}). Then, as a special case of the section formulae, the midpoint of *AB* has coordinates (½(*x*_{1}+*x*_{2}) ½(*y*_{1}+*y*_{2}). For points *A* and *B* in 3-dimensional space, with Cartesian coordinates (*x*_{1}, *y*_{1}, *z*_{1}) and (*x*_{2}, *y*_{2}, *z*_{2}), the midpoint of *AB* has coordinates

(½(*x*_{1}+*x*_{2}), ½(*y*_{1}+*y*_{2}), ½(*z*_{1}+*z*_{2}).

If points *A* and *B* have position vectors **a** and **b**, the midpoint of *AB* has position vector ½(**a**+**b**).

*Subjects:*
Mathematics — Chemistry.

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