TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App 45
The
Inverse
tool constructs an inverse point with respect to a circle
and a point, according to the equation
OM
ø
OM’ = r
2
where:
M
and
M’
are points that lie on a ray with endpoint
O
.
O
= center of circle.
M
= selected point.
M’
= inverse point.
r
= radius of selected circle.
As the selected point approaches the center point, the inverse point
approaches a point at infinity. If
M
is defined to be on a line, the
locus of
M’
constructs a circle that passes through the center of the
original circle.
If the original point lies in the interior of the circle, the inverse point
is constructed in the exterior, and vice versa. The inverse point lies
on a ray with the center point as the endpoint.
1.
Create a circle and a point as shown
in this example.
2.
Press
‡
and select
6:Inverse
.
3.
Select the point as the original point.
Select a point.
4.
Select the circle.
Select a circle.
An inverse point is created.
You can modify an inverse point by dragging the point or by
modifying the circle that defines it.
1.
Grab and drag the original point.
The inverse point inside the circle
moves according to the changed
position of the original point.
The inverse point is modified.
Creating Reflections and Inverse Objects
(continued)
Creating an Inverse
Point
Modifying an
Inverse Point
Note:
Because an inverse
point is a dependent point,
ou cannot change it
directly.
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