reflection - Maple Help

geometry

 reflection
 find the reflection of a geometric object with respect to a given point or line

 Calling Sequence reflection(Q, P, c)

Parameters

 Q - the name of the object to be created P - geometric object c - point or line

Description

 • Let c be a fixed point in the plane. By the reflection (or half-turn) $R\left(c\right)$ in  point c we mean the transformation of the plane S onto itself which carries each point P of the plane into the point Q of the plane such that c is the midpoint of PQ. Point c is called the center of the reflection.
 • Let c be a fixed line in the plane. By the reflection $R\left(c\right)$ about line c we mean the transformation of the plane S onto itself which carries each point P of the plane into the point Q of the plane such that c goes through the midpoint of PQ and is perpendicular to PQ.
 • For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))
 • The command with(geometry,reflection) allows the use of the abbreviated form of this command.

Examples

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

reflection of a point with respect to a line

 > $\mathrm{point}\left(P,2,3\right),\mathrm{line}\left(l,a+b=1,\left[a,b\right]\right)$
 ${P}{,}{l}$ (1)
 > $\mathrm{reflection}\left(Q,P,l\right)$
 ${Q}$ (2)
 > $\mathrm{coordinates}\left(Q\right)$
 $\left[{-2}{,}{-1}\right]$ (3)

reflection of a line with respect to a line

 > $\mathrm{line}\left(\mathrm{x_axis},y=0,\left[x,y\right]\right):$
 > $\mathrm{reflection}\left(\mathrm{l1},l,\mathrm{x_axis}\right):$
 > $\mathrm{draw}\left(\left[l,\mathrm{l1}\right]\right)$

reflection of a circle with respect to a line

 > $\mathrm{circle}\left(c,\left[\mathrm{point}\left(\mathrm{OO},0,0\right),1\right]\right):$
 > $\mathrm{detail}\left(c\right)$
 assume that the names of the horizontal and vertical axes are _x and _y, respectively
 $\begin{array}{ll}{\text{name of the object}}& {c}\\ {\text{form of the object}}& {\mathrm{circle2d}}\\ {\text{name of the center}}& {\mathrm{OO}}\\ {\text{coordinates of the center}}& \left[{0}{,}{0}\right]\\ {\text{radius of the circle}}& {1}\\ {\text{equation of the circle}}& {{\mathrm{_x}}}^{{2}}{+}{{\mathrm{_y}}}^{{2}}{-}{1}{=}{0}\end{array}$ (4)
 > $\mathrm{line}\left(\mathrm{l1},\left[\mathrm{point}\left(\mathrm{a1},1,0\right),\mathrm{point}\left(\mathrm{a2},0,1\right)\right]\right):$
 > $\mathrm{line}\left(\mathrm{l2},\left[\mathrm{point}\left(\mathrm{b1},-1,0\right),\mathrm{point}\left(\mathrm{b2},0,1\right)\right]\right):$
 > $\mathrm{line}\left(\mathrm{l3},\left[\mathrm{point}\left(\mathrm{c1},-1,0\right),\mathrm{point}\left(\mathrm{c2},0,-1\right)\right]\right):$
 > $\mathrm{line}\left(\mathrm{l4},\left[\mathrm{point}\left(\mathrm{d1},0,-1\right),\mathrm{point}\left(\mathrm{d2},1,0\right)\right]\right):$
 > $\mathrm{reflection}\left(\mathrm{c1},c,\mathrm{l1}\right):$$\mathrm{reflection}\left(\mathrm{c2},c,\mathrm{l2}\right):$
 > $\mathrm{reflection}\left(\mathrm{c3},c,\mathrm{l3}\right):$$\mathrm{reflection}\left(\mathrm{c4},c,\mathrm{l4}\right):$
 > $\mathrm{draw}\left(\left\{\mathrm{c1},\mathrm{c2},\mathrm{c3},\mathrm{c4},c\left(\mathrm{color}=\mathrm{orange}\right)\right\},\mathrm{color}=\mathrm{blue},\mathrm{axes}=\mathrm{BOX},\mathrm{style}=\mathrm{POINT},\mathrm{symbol}=\mathrm{DIAMOND}\right)$