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geometry

 translation
 find the translation of a geometric object with respect to a directed segment

 Calling Sequence translation(Q, obj, AB)

Parameters

 Q - the name of the object to be created obj - geometric object AB - directed segment

Description

 • Let AB be a directed line segment in the plane S. By the translation $T\left(\mathrm{AB}\right)$ we mean the transformation of S onto itself which carries each point P of the plane into the point P1 of the plane such that the directed line segment PP1 is equal and parallel to the directed segment AB.
 • The directed segment AB is called the vector of the translation.
 • For a detailed description of Q (the object created), use the routine detail (i.e., detail(Q))
 • The command with(geometry,translation) allows the use of the abbreviated form of this command.

Examples

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

Translation of a point

 > $\mathrm{point}\left(A,0,0\right):$$\mathrm{dsegment}\left(\mathrm{dsg},\mathrm{point}\left(M,0,0\right),\mathrm{point}\left(N,1,0\right)\right):$
 > $\mathrm{translation}\left(\mathrm{Atra},A,\mathrm{dsg}\right):$
 > $\mathrm{coordinates}\left(\mathrm{Atra}\right)$
 $\left[{1}{,}{0}\right]$ (1)

translation of a circle

 > $\mathrm{circle}\left(c,\left[\mathrm{point}\left(\mathrm{OO},0,0\right),1\right]\right):$
 > $\mathrm{translation}\left(\mathrm{ctra1},c,\mathrm{dsg}\right):$
 > $\mathrm{detail}\left(\left\{c,\mathrm{ctra1}\right\}\right)$
 assume that the names of the horizontal and vertical axes are _x and _y, respectively assume that the names of the horizontal and vertical axes are _x and _y, respectively
 $\left\{\begin{array}{ll}{\text{name of the object}}& {c}\\ {\text{form of the object}}& {\mathrm{circle2d}}\\ {\text{name of the center}}& {\mathrm{OO}}\\ {\text{coordinates of the center}}& \left[{0}{,}{0}\right]\\ {\text{radius of the circle}}& {1}\\ {\text{equation of the circle}}& {{\mathrm{_x}}}^{{2}}{+}{{\mathrm{_y}}}^{{2}}{-}{1}{=}{0}\end{array}{,}\begin{array}{ll}{\text{name of the object}}& {\mathrm{ctra1}}\\ {\text{form of the object}}& {\mathrm{circle2d}}\\ {\text{name of the center}}& {\mathrm{center_ctra1}}\\ {\text{coordinates of the center}}& \left[{1}{,}{0}\right]\\ {\text{radius of the circle}}& {1}\\ {\text{equation of the circle}}& {{\mathrm{_x}}}^{{2}}{+}{{\mathrm{_y}}}^{{2}}{-}{2}{}{\mathrm{_x}}{=}{0}\end{array}\right\}$ (2)
 > $\mathrm{translation}\left(\mathrm{ctra2},c,\mathrm{dsegment}\left(\mathrm{dsg2},M,\mathrm{point}\left(\mathrm{N1},0,1\right)\right)\right):$
 > $\mathrm{translation}\left(\mathrm{ctra3},c,\mathrm{dsegment}\left(\mathrm{dsg3},M,\mathrm{point}\left(\mathrm{N2},-1,0\right)\right)\right):$
 > $\mathrm{translation}\left(\mathrm{ctra4},c,\mathrm{dsegment}\left(\mathrm{dsg4},M,\mathrm{point}\left(\mathrm{N3},0,-1\right)\right)\right):$
 > $\mathrm{draw}\left(\left\{\mathrm{ctra1},\mathrm{ctra2},\mathrm{ctra3},\mathrm{ctra4},c\left(\mathrm{style}=\mathrm{LINE},\mathrm{numpoints}=200\right)\right\},\mathrm{axes}=\mathrm{BOX},\mathrm{style}=\mathrm{POINT},\mathrm{title}=\mathrm{translation of a circle}\right)$