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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);)

The command with(geom3d,altitude) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geom3d}\right)\:$

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

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

$\mathrm{hA1}$

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

$\mathrm{line3d}$

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

Warning, assume that the parameter in the parametric equations is _t

Warning, assuming that the names of the axes are _x, _y, and _z

$\begin{array}{cc}\text{name of the object}& \mathrm{hA1}\\ \text{form of the object}& \mathrm{line3d}\\ \text{equation of the line}& \left[\mathrm{\_x}=\frac{9\mathrm{\_t}}{5}\,\mathrm{\_y}=\frac{3\mathrm{\_t}}{5}\,\mathrm{\_z}=0\right]\end{array}$

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

$\mathrm{hA2}$

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

$\mathrm{segment3d}$

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

$\begin{array}{cc}\text{name of the object}& \mathrm{hA2}\\ \text{form of the object}& \mathrm{segment3d}\\ \text{the 2 ends of the segment}& \left[\left[0\,0\,0\right]\,\left[\frac{9}{5}\,\frac{3}{5}\,0\right]\right]\end{array}$

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

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