find the stretch-reflection of a geometric object
StretchReflection(Q, P, l, O, k )
the name of the object to be created
point on l
number which is the ratio of the stretch-reflection
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⁡O,k,l we mean the product R⁡lH⁡O,k where R⁡l is the reflection with respect to line l, and H⁡O,k 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.
Assign the name of the horizontal and vertical axis:
_EnvHorizontalName ≔ a:_EnvVerticalName ≔ b:
dilate p with center A and ratio 1/2, then reflect this object with respect to the line l
name of the objectpform of the objectparabola2dvertex0,0focus0,14directrixb+14=0equation of the parabola−a2+b=0,name of the objectp1form of the objectparabola2dvertex0,0focus0,−18directrix−2⁢b+14=0equation of the parabola−4⁢a2−2⁢b=0
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