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geom3d

 altitude
 find the altitude of a given triangle

 Calling Sequence altitude(hA, A, ABC, H)

Parameters

 hA - the A-altitude of ABC A - vertex of ABC ABC - triangle H - (optional) name

Description

 • 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.

Examples

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

Define triangle ABC with vertices A, B and C.

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

Find the altitude of ABC at A

 > $\mathrm{altitude}\left(\mathrm{hA1},A,\mathrm{ABC}\right)$
 ${\mathrm{hA1}}$ (1)
 > $\mathrm{form}\left(\mathrm{hA1}\right)$
 ${\mathrm{line3d}}$ (2)
 > $\mathrm{detail}\left(\mathrm{hA1}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{hA1}}\\ {\text{form of the object}}& {\mathrm{line3d}}\\ {\text{equation of the line}}& \left[{\mathrm{_x}}{=}\frac{{9}{}{\mathrm{_t}}}{{5}}{,}{\mathrm{_y}}{=}\frac{{3}{}{\mathrm{_t}}}{{5}}{,}{\mathrm{_z}}{=}{0}\right]\end{array}$ (3)
 > $\mathrm{altitude}\left(\mathrm{hA2},A,\mathrm{ABC},H\right)$
 ${\mathrm{hA2}}$ (4)
 > $\mathrm{form}\left(\mathrm{hA2}\right)$
 ${\mathrm{segment3d}}$ (5)
 > $\mathrm{detail}\left(\mathrm{hA2}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{hA2}}\\ {\text{form of the object}}& {\mathrm{segment3d}}\\ {\text{the 2 ends of the segment}}& \left[\left[{0}{,}{0}{,}{0}\right]{,}\left[\frac{{9}}{{5}}{,}\frac{{3}}{{5}}{,}{0}\right]\right]\end{array}$ (6)
 > $\mathrm{DefinedAs}\left(\mathrm{hA2}\right)$
 $\left[{A}{,}{H}\right]$ (7)