State whether the transformation of a Preimage and Image circles appears to be a rigid motion?Explain
To determine whether the transformation of a preimage and image circles appears to be a rigid motion, you need to consider if the transformation preserves distance and shape.
A rigid motion, also known as an isometry, is a transformation that preserves the distance between points, as well as the size and shape of objects. In other words, if you measure the distance between any two points in the preimage, it should be the same as the distance between the corresponding points in the image.
For circles specifically, a rigid motion would mean that the transformed image of a circle would still have the same size and shape as the preimage circle. The center of the circle would remain the same, and the radius would not be affected.
To determine if a transformation qualifies as a rigid motion, you can follow these steps:
1. Identify the preimage and image circles.
2. Select two points on the preimage circle.
3. Measure the distance between these two points using a ruler or any measuring tool.
4. Apply the transformation to the preimage.
5. Locate the corresponding points on the image circle.
6. Measure the distance between these two points on the image circle.
7. Compare the measured distances from steps 3 and 6.
If the distances are the same (or very close) in both the preimage and image, then the transformation can be considered a rigid motion. However, if the distances are different, it indicates that the transformation does not preserve distance and, therefore, is not a rigid motion.