An altitude from the vertex A of a triangle ABC is a line segment (or its extension) from vertex A perpendicular to the side BC.

If the optional argument H is given, the object returned (hA) is a line segment AH where H is the projection of A onto the side BC. If it is not given, the object returned is a line passing through A and is perpendicular to the side BC.

For a detailed description of the altitude hA, use the routine detail (i.e., detail(hA))

Note that the routine only works if the vertices of the triangle are known.

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

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

$\mathrm{triangle}\left(\mathrm{ABC}\,\left[\mathrm{point}\left(A\,0\,0\right)\,\mathrm{point}\left(B\,2\,0\right)\,\mathrm{point}\left(C\,1\,3\right)\right]\right)\:$

$\mathrm{altitude}\left(\mathrm{hA1}\,A\,\mathrm{ABC}\right)$

$\mathrm{hA1}$

$\mathrm{form}\left(\mathrm{hA1}\right)$

$\mathrm{line2d}$

$\mathrm{detail}\left(\mathrm{hA1}\right)$

assume that the names of the horizontal and vertical axes are _x and _y, respectively

$\begin{array}{ll}\text{name of the object}& \mathrm{hA1}\\ \text{form of the object}& \mathrm{line2d}\\ \text{equation of the line}& -\mathrm{\_x}+3\mathrm{\_y}=0\end{array}$

$\mathrm{altitude}\left(\mathrm{hA2}\,A\,\mathrm{ABC}\,H\right)$

$\mathrm{hA2}$

$\mathrm{form}\left(\mathrm{hA2}\right)$

$\mathrm{segment2d}$

$\mathrm{detail}\left(\mathrm{hA2}\right)$

$\begin{array}{ll}\text{name of the object}& \mathrm{hA2}\\ \text{form of the object}& \mathrm{segment2d}\\ \text{the two ends of the segment}& \left[\left[0\,0\right]\,\left[\frac{9}{5}\,\frac{3}{5}\right]\right]\end{array}$

$\mathrm{DefinedAs}\left(\mathrm{hA2}\right)$

$\left[A\,H\right]$