This command returns true if the point lies on the line segment and false if it does not.  It first checks if they are collinear using PointOrientation and then checks if the point in within the bounding box given by the endpoints of the line segment.

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

$a≔\left[0\,0\right]\;$$b≔\left[1\,1\right]\;$$c≔\left[0.4\,0.4\right]\;$$d≔\left[1.1\,1.1\right]\;$$e≔\left[0.5\,0.55\right]$

$a≔\left[0\,0\right]$

$b≔\left[1\,1\right]$

$c≔\left[0.4\,0.4\right]$

$d≔\left[1.1\,1.1\right]$

$e≔\left[0.5\,0.55\right]$

$\mathrm{plots}:-\mathrm{display}\left(\mathrm{plottools}:-\mathrm{point}\left(\left[a\,b\,c\,d\,e\right]\,\mathrm{symbolsize}=20\right)\,\mathrm{plots}:-\mathrm{textplot}\left(\left[c\left[\right]\,''c''\right]\,\mathrm{align}=\left[''above''\,''left''\right]\right)\,\mathrm{plots}:-\mathrm{textplot}\left(\left[d\left[\right]\,''d''\right]\,\mathrm{align}=\left[''below''\,''left''\right]\right)\,\mathrm{plots}:-\mathrm{textplot}\left(\left[e\left[\right]\,''e''\right]\,\mathrm{align}=\left[''above''\,''left''\right]\right)\,\mathrm{plottools}:-\mathrm{line}\left(a\,b\right)\,\mathrm{axes}=\mathrm{box}\right)$

$\mathrm{PointOnSegment}\left(c\,\left[a\,b\right]\right)$

$\mathrm{true}$

$\mathrm{PointOnSegment}\left(d\,\left[a\,b\right]\right)$

$\mathrm{false}$

$\mathrm{PointOnSegment}\left(e\,\left[a\,b\right]\right)$

$\mathrm{false}$

$M≔\mathrm{Array}\left(\left[a\,b\,c\,d\,e\right]\,\mathrm{datatype}=\mathrm{float}\left[8\right]\,\mathrm{order}=\mathrm{C\_order}\right)$

$M≔\left[\begin{array}{cc}0.& 0.\\ 1.& 1.\\ 0.400000000000000& 0.400000000000000\\ 1.10000000000000& 1.10000000000000\\ 0.500000000000000& 0.550000000000000\end{array}\right]$

$\mathrm{PointOnSegment}\left(M\,\left[3\,1\,2\right]\right)$

$\mathrm{true}$

$\mathrm{PointOnSegment}\left(M\,\left[5\,1\,2\right]\right)$

$\mathrm{false}$

The ComputationalGeometry[PointOnSegment] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.