# Rotation about a Point

- Author:
- LHasty

- Topic:
- Coordinates, Rotation

Rotation is a Rigid-Motion Transformation
about a Point of Rotation at a given Angle of Rotation.
Triangle ABC is rotated about Point O (0,0)
Move Slider α for an Angle of Rotation between 0° and 360°.

1. What kind of a triangle is ABC ? _____________________________________.
2. What are the Coordinates for Points A, B, and C?
Point A ( _____ , _____ ), Point B ( _____ , _____ ), and Point C ( _____ , _____ ).
3. Move the slider to 90°, what are the Coordinates for Points A’, B’, and C’?
Point A’ ( _____ , _____ ), Point B’ ( _____ , _____ ), and Point C’ ( _____ , _____ ).
4. Move the slider to 180°, what are the Coordinates for Points A’, B’, and C’?
Point A’ ( _____ , _____ ), Point B’ ( _____ , _____ ), and Point C’ ( _____ , _____ ).
5. Move the slider to 270°, what are the Coordinates for Points A’, B’, and C’?
Point A’ ( _____ , _____ ), Point B’ ( _____ , _____ ), and Point C’ ( _____ , _____ ).
6. Compare and contrast coordinates for the above rotations:
What remained the same _______________________________________________________
What changed? _______________________________________________________
7. What do you notice about the slopes of the side AB and side BC ?
____________________________________________________________________________________
8. Move Point A to change the orientation of the triangle ABC.
Is the above relationship between coordinate points the same?
What is Different ? ______________________________________________________________
____________________________________________________________________________________
Next, be sure pre-image and rotated image is not onto itself (rotate 90°).
Place cursor on A’ of rotated image, touch trackpad with two fingers for additional options, and select [Trace on],
repeat for points B’ and C’.
Place cursor on slider α, touch trackpad with two fingers for additional options, and select [Animation On] .
What relationship exist between the pre-image points and the rotated image points with respect to the origin ?
__________________________________________________________________________________________
To reset Trace, deselect [Animation On] and use two fingers on trackpad to scroll in or out.
Move the Point of Rotation away from the origin.
Does the same relationship exist between the pre-image points and the rotated image points with respect to the origin ?
__________________________________________________________________________________________