The routine computes the distance between two points P1 and P2 or between a point P1 and a line l.

The command with(geometry,distance) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{point}\left(A\,a\,b\right),\mathrm{point}\left(B\,c\,d\right)\:$

$\mathrm{distance}\left(A\,B\right)$

$\sqrt{{\left(a-c\right)}^2+{\left(b-d\right)}^2}$

$\mathrm{assume}\left(m\ne 0\right)\:$

$\mathrm{line}\left(l\,mx+ny=w\,\left[x\,y\right]\right)\:$

$\mathrm{distance}\left(A\,l\right)$

$\frac{\left|a\mathrm{m~}+bn-w\right|}{\sqrt{{\mathrm{m~}}^2+n^2}}$

$\mathrm{distance}\left(B\,l\right)$

$\frac{\left|c\mathrm{m~}+dn-w\right|}{\sqrt{{\mathrm{m~}}^2+n^2}}$