OnSegment - Maple Help
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geom3d

 OnSegment
 Find the point which divides the segment joining two given points by some ratio

 Calling Sequence OnSegment(C, A, B, k) OnSegment(C, seg, k)

Parameters

 C - the name of the point to be created A, B - two points seg - segment k - ratio

Description

 • The routine returns point C which is the point lying on the segment defined by two points A, B with ratio k
 • For a detailed description of point C, use the routine detail (i.e., detail(C))
 • The command with(geom3d,OnSegment) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{assume}\left(a,\mathrm{real},b,\mathrm{real},c,\mathrm{real},d,\mathrm{real},a\ne c,k,\mathrm{real}\right)$
 > $\mathrm{point}\left(A,a,b,1\right),\mathrm{point}\left(B,c,d,5\right):$
 > $\mathrm{OnSegment}\left(C,A,B,k\right)$
 > $\mathrm{additionally}\left(k\ne -1\right)$
 > $\mathrm{OnSegment}\left(C,A,B,k\right)$
 ${C}$ (1)
 > $\mathrm{coordinates}\left(C\right)$
 $\left[\frac{{\mathrm{c~}}{}{\mathrm{k~}}{+}{\mathrm{a~}}}{{\mathrm{k~}}{+}{1}}{,}\frac{{\mathrm{d~}}{}{\mathrm{k~}}{+}{\mathrm{b~}}}{{\mathrm{k~}}{+}{1}}{,}\frac{{1}{+}{5}{}{\mathrm{k~}}}{{\mathrm{k~}}{+}{1}}\right]$ (2)