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Let A and B be points in the plane with Cartesian coordinates (x1, y1) and (x2, y2). Then, as a special case of the section formulae, the midpoint of AB has coordinates (½(x1+x2) ½(y1+y2). For points A and B in 3-dimensional space, with Cartesian coordinates (x1, y1, z1) and (x2, y2, z2), the midpoint of AB has coordinates

(½(x1+x2), ½(y1+y2), ½(z1+z2).

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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