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geometry

 rotation
 find the rotation of a geometric object with respect to a given point

 Calling Sequence rotation(Q, P, g, co, R)

Parameters

 Q - the name of the object to be created P - geometric object g - the angle of rotation co - the direction of rotation, either clockwise or counterclockwise R - (optional) the center of rotation

Description

 • Let R be a fixed point of the plane, g and co denote the sensed angle. By the rotation $R\left(\mathrm{O},g,\mathrm{co}\right)$ 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 OP1 = OP and the angle $\mathrm{POP1}=g$ in the direction specified by co.
 • Point O is called the center of the rotation, and g is called the angle of the rotation.
 • If the fifth argument is omitted, then the origin is the center of rotation.
 • For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))
 • The command with(geometry,rotation) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{point}\left(P,2,0\right),\mathrm{point}\left(Q,1,0\right)$
 ${P}{,}{Q}$ (1)
 > $\mathrm{rotation}\left(\mathrm{P1},P,\mathrm{π},'\mathrm{counterclockwise}'\right)$
 ${\mathrm{P1}}$ (2)
 > $\mathrm{coordinates}\left(\mathrm{P1}\right)$
 $\left[{-}{2}{,}{0}\right]$ (3)
 > $\mathrm{rotation}\left(\mathrm{P2},P,\frac{\mathrm{π}}{2},'\mathrm{clockwise}',Q\right)$
 ${\mathrm{P2}}$ (4)
 > $\mathrm{coordinates}\left(\mathrm{P2}\right)$
 $\left[{1}{,}{-}{1}\right]$ (5)
 > $f≔{y}^{2}=x:$$\mathrm{parabola}\left(p,f,\left[x,y\right]\right):$
 > $\mathrm{point}\left(\mathrm{OO},0,0\right):$
 > $\mathrm{rotation}\left(\mathrm{p1},p,\frac{\mathrm{π}}{2},'\mathrm{counterclockwise}',\mathrm{OO}\right):$
 > $\mathrm{detail}\left(\left\{\mathrm{p1},p\right\}\right)$
 $\left\{\begin{array}{ll}{\text{name of the object}}& {p}\\ {\text{form of the object}}& {\mathrm{parabola2d}}\\ {\text{vertex}}& \left[{0}{,}{0}\right]\\ {\text{focus}}& \left[\frac{{1}}{{4}}{,}{0}\right]\\ {\text{directrix}}& {x}{+}\frac{{1}}{{4}}{=}{0}\\ {\text{equation of the parabola}}& {{y}}^{{2}}{-}{x}{=}{0}\end{array}{,}\begin{array}{ll}{\text{name of the object}}& {\mathrm{p1}}\\ {\text{form of the object}}& {\mathrm{parabola2d}}\\ {\text{vertex}}& \left[{0}{,}{0}\right]\\ {\text{focus}}& \left[{0}{,}\frac{{1}}{{4}}\right]\\ {\text{directrix}}& {y}{+}\frac{{1}}{{4}}{=}{0}\\ {\text{equation of the parabola}}& {{x}}^{{2}}{-}{y}{=}{0}\end{array}\right\}$ (6)
 > $\mathrm{rotation}\left(\mathrm{p2},p,\mathrm{π},'\mathrm{counterclockwise}',\mathrm{OO}\right):$
 > $\mathrm{rotation}\left(\mathrm{p3},p,\frac{\mathrm{π}}{2},'\mathrm{clockwise}',\mathrm{OO}\right):$
 > $\mathrm{draw}\left(\left[p\left(\mathrm{style}=\mathrm{LINE},\mathrm{thickness}=2\right),\mathrm{p1},\mathrm{p2},\mathrm{p3}\right],\mathrm{style}=\mathrm{POINT},\mathrm{symbol}=\mathrm{DIAMOND},\mathrm{color}=\mathrm{green},\mathrm{title}=\mathrm{rotation of a parabola}\right)$

 See Also

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