Google Classroom
GeoGebraGeoGebra Classroom

How do figures rotate on a plane?


Click the link below to see how to use the needed tools.

Explore this rotation and measure the angles made between the pre-image points, the point of rotation and the corresponding image points using the angle tool. What do you notice? Write your response in the box below.

What do you notice about the angles made with corresponding pre-image and image points using the center of rotation as the vertex of the angle?

In the interactive below 3 points are rotated 45, 90 and 180 degrees clockwise around the origin (start at 1 and go through each iteration by pressing the right double arrow). Watch as the rotations occur and make some observations.

General observations

What did you notice about the location of each point compared to the other points as they were rotated by the same amount?

Making connections

In the interactive above individual points were rotated by the same amount. Based on your observations of those points, how do you think you would rotate a triangle or any figure with multiple points and sides around a center of rotation?

Rotate triangle ABC counterclockwise 60 degrees around center point D. The video from the link below shows you how to use the tools.

180 Degree rotation v Reflection

Reflect triangle ABC across line T. Next rotate triangle ABC 180 degrees clockwise around point k. Answer the questions below to compare these two moves.

Reflection vs 180 degree Rotation

Examining at the reflection compared to a 180 degree rotation below. What are some differences you notice? How could you identify the difference between a 180 degree rotation and a reflection?

Identifying key characteristics of reflections

Move the line of reflection to different positions. What do you notice to be always true about the corresponding pre image and image points compared to the line of reflection?

Based on the two answers above and your experience define a reflection (you must reference the line of reflection, pre-image points and image points).