Rotation Patterns

Rotate a Figure about a Point on the Figure.

(A). In the applet below is a right isosceles triangle. Perform the following operations:

• Rotate triangle ABC 90 degrees clockwise around B.
• Rotate triangle ABC 180 degrees around B.
• Rotate triangle ABC 270 degrees clockwise around B.

What would it look like when you rotate the triangle 4 times around B:

(1). through 90 degrees clockwise? 

(2). through180 degrees clockwise?

(3). through 270 degrees clockwise?

(B). In the applet below is a right isosceles triangle. Perform the following operations:

• Rotate triangle ABC 90 degrees clockwise around A.
• Rotate triangle ABC 180 degrees around A.
• Rotate triangle ABC 270 degrees clockwise around A.

Rotate a Line Segment about a Point.

(A). In the applet below is a line segment CD. Perform the following operations:

• Rotate segment CD 180 degrees around point D.
• Rotate segment CD 180 degrees around point E.
• Rotate segment CD 180 degrees around point M.

Rotate a Line Segment about a Point.

• Create a segment AB and a point C that is not on segment AB.
• Rotate segment AB 180 degrees around point B.
• Rotate segment AB 180 degrees around point C.
• Construct the midpoint of segment AB with the midpoint tool
• Rotate segment AB 180 degrees around its midpoint.

(1). What is the image of A?

(2). What happens when you rotate a segment 180 degrees?

Describe a sequence of transformations that takes to .

Here are two line segments:

Is it possible to rotate one line segment to the other? If so, find the center of such a rotation. If not, explain why not.

Here is a diagram built with three different rigid transformations of triangle ABC.

(1). Describe a rigid transformation that takes triangle  ABC  to triangle  CDE.

(2). Describe a rigid transformation that takes triangle  ABC  to triangle  EFG.

(3). Describe a rigid transformation that takes triangle  ABC  to triangle  GHA.