Texas Instruments TI-89 User Manual page 49

Creating Reflections and Inverse Objects
Creating an Inverse
Point
Modifying an
Inverse Point
Note: Because an inverse
point is a dependent point,
you cannot change it
directly.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Cabri Geometry App
The tool constructs an inverse point with respect to a circle
Inverse
and a point, according to the equation
where:
and are points that lie on a ray with endpoint
M M'
= center of circle.
O
= selected point.
M
= inverse point.
M'
= radius of selected circle.
r
As the selected point approaches the center point, the inverse point
approaches a point at infinity. If
locus of constructs a circle that passes through the center of the
M'
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.
4. Select the circle.
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.
(continued)
2
OM ø OM' = r
.
O
is defined to be on a line, the
M
.
Select a point.
Select a circle.
An inverse point is created.
The inverse point is modified.
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