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.

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

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

$P,l$

$\mathrm{reflection}\left(Q\,P\,l\right)$

$Q$

$\mathrm{coordinates}\left(Q\right)$

$\left[\mathrm{-2}\,\mathrm{-1}\right]$

$\mathrm{line}\left(\mathrm{x\_axis}\,y=0\,\left[x\,y\right]\right)\:$

$\mathrm{reflection}\left(\mathrm{l1}\,l\,\mathrm{x\_axis}\right)\:$

$\mathrm{draw}\left(\left[l\,\mathrm{l1}\right]\right)$

$\mathrm{circle}\left(c\,\left[\mathrm{point}\left(\mathrm{OO}\,0\,0\right)\,1\right]\right)\:$

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

assume that the names of the horizontal and vertical axes are _x and _y, respectively

$\begin{array}{ll}\text{name of the object}& c\\ \text{form of the object}& \mathrm{circle2d}\\ \text{name of the center}& \mathrm{OO}\\ \text{coordinates of the center}& \left[0\,0\right]\\ \text{radius of the circle}& 1\\ \text{equation of the circle}& {\mathrm{\_x}}^2+{\mathrm{\_y}}^2-1=0\end{array}$

$\mathrm{line}\left(\mathrm{l1}\,\left[\mathrm{point}\left(\mathrm{a1}\,1\,0\right)\,\mathrm{point}\left(\mathrm{a2}\,0\,1\right)\right]\right)\:$

$\mathrm{line}\left(\mathrm{l2}\,\left[\mathrm{point}\left(\mathrm{b1}\,-1\,0\right)\,\mathrm{point}\left(\mathrm{b2}\,0\,1\right)\right]\right)\:$

$\mathrm{line}\left(\mathrm{l3}\,\left[\mathrm{point}\left(\mathrm{c1}\,-1\,0\right)\,\mathrm{point}\left(\mathrm{c2}\,0\,-1\right)\right]\right)\:$

$\mathrm{line}\left(\mathrm{l4}\,\left[\mathrm{point}\left(\mathrm{d1}\,0\,-1\right)\,\mathrm{point}\left(\mathrm{d2}\,1\,0\right)\right]\right)\:$

$\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)\:$

$\mathrm{draw}\left(\left\{\mathrm{c1}\,\mathrm{c2}\,\mathrm{c3}\,\mathrm{c4}\,c\left(\mathrm{color}=\mathrm{orange}\right)\right\}\,\mathrm{color}=\mathrm{blue}\,\mathrm{axes}=\mathrm{BOX}\,\mathrm{style}=\mathrm{POINT}\,\mathrm{symbol}=\mathrm{DIAMOND}\right)$