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The **distance** between two points in the plane is the **length
of the line segment** joining the two points. If the points have
**cartesian coordinates** (*x*,*y*) and (*x*,*y*), this distance
is

If the points have **polar coordinates** (*r*,) and
(*r*,), this distance is

If the points have **oblique coordinates** (*x*,*y*) and
(*x*,*y*), this distance is

where is the angle between the axes (Figure 1.5.1 ).

The point *k*% of the way from *P*=(*x*,*y*) to *P*=(*x*,*y*) is

(The same formula works also in oblique coordinates.) This point
divides the segment *P**P* in the ratio *k*:(100-*k*). As a
particular case, the **midpoint** of *P**P* is given by

(½(*x*+*x*), ½(*y*+*y*)).

The **distance** from the point (*x*,*y*) to the line *ax*+*by*+*c*=0 is

*Silvio Levy
Wed Oct 4 16:41:25 PDT 1995*

This document is excerpted from the 30th Edition of the *CRC Standard Mathematical Tables and Formulas* (CRC Press). Unauthorized duplication is forbidden.