Let l be a fixed line of the plane and O a fixed point on l, and let k be a given nonzero real number. By the stretch-reflection $S\left(\mathrm{O}\,k\,l\right)$ we mean the product $R\left(l\right)H\left(\mathrm{O},k\right)$ where $R\left(l\right)$ is the reflection with respect to line l, and $H\left(\mathrm{O}\,k\right)$ is the dilatation with center O and ratio k. The line l is called the axis of the stretch-reflection, the point O is called the center of the stretch-reflection, and k is called the ratio of the stretch-reflection

For a detailed description of Q (the object created), use the routine detail (i.e., detail(Q))

The command with(geometry,StretchReflection) allows the use of the abbreviated form of this command.

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

$\mathrm{\_EnvHorizontalName}≔a\:$$\mathrm{\_EnvVerticalName}≔b\:$

$\mathrm{parabola}\left(p\,b=a^2\right)\:$

$\mathrm{point}\left(A\,0\,0\right),\mathrm{line}\left(l\,b=0\right)\:$

$\mathrm{StretchReflection}\left(\mathrm{p1}\,p\,l\,A\,\frac{1}{2}\right)\:$

$\mathrm{detail}\left(\left\{p\,\mathrm{p1}\right\}\right)$

$\left\{\begin{array}{ll}\text{name of the object}& p\\ \text{form of the object}& \mathrm{parabola2d}\\ \text{vertex}& \left[0\,0\right]\\ \text{focus}& \left[0\,\frac{1}{4}\right]\\ \text{directrix}& b+\frac{1}{4}=0\\ \text{equation of the parabola}& -a^2+b=0\end{array}\,\begin{array}{ll}\text{name of the object}& \mathrm{p1}\\ \text{form of the object}& \mathrm{parabola2d}\\ \text{vertex}& \left[0\,0\right]\\ \text{focus}& \left[0\,-\frac{1}{8}\right]\\ \text{directrix}& -2b+\frac{1}{4}=0\\ \text{equation of the parabola}& -4a^2-2b=0\end{array}\right\}$

$\mathrm{draw}\left(\left\{p\left(\mathrm{style}=\mathrm{LINE}\right)\,\mathrm{p1}\left(\mathrm{style}=\mathrm{POINT}\right)\right\}\right)$