*Once you can construct the inverse of a given point P with
respect to gamma, you can turn your attention to inverting entire geometric
figures. The Inverting Geometric Figures Menu on the previous page contains
links to four files created
with
Geometer's
Sketchpad.
These
files give the user the ability to animate P along the path of the figure
to be inverted and traces the path of P'. By clicking on the page tabs
at the bottom of each sketch, the user can explore different sets of given
conditions. These sketches can be used by teachers and students as a way
to make and test their conjectures. Questions and
activities
for students
are
listed
below.*

**Circles**

__1. For each of the provided sketches, make conjectures about the path of
P'. Test and revise your conjectures by animating P.__

__2. How does the position of the circle with respect to gamma affect its
inverse?__

__3. How does the size of the circle with respect to gamma affect its inverse?__

**Lines**

__1. For each of the provided sketches, make conjectures about the path of
P'. Test and revise your conjectures by animating P.__

__2. How does the position of the line with respect to gamma affect its inverse?__

**More Circles**

__1. For each of the provided sketches, make conjectures about the path of
P'. Test and revise your conjectures by animating P.__

**Other Conic Sections**

__2. How does the position of the conic section with respect to gamma affect
its inverse?__

__3. How does altering the shape (by changing the focal distance) of each
conic section affect its inverse?__

*In some cases, one of these sketches could occupy your students for an
entire lesson. Others are merely worth a look before moving on. The depth
at which
you direct
your
students to investigate depends upon your assessment of your students' needs,
abilities, and interest. If your students have a strong background, they
may wish to verify their conjectures using analytic geometry.*

**Return to Geometric Inversion Homepage**