Question

A student claimed that the transformation (x, y) arrowright (3x, y) is a rigid motion because the segment joining (6, 1) to (6, 3) is transformed to the segment joining (18, 1) to (18, 3), and both of these segments have the same length. Complete the explanation of the student's error.



The transformation is a stretch by a factor of , so it preserves the length of segments but not the length of segments. In order to be a rigid motion, the transformation must preserve lengths, so this transformation a rigid motion.

Answer 1

A rigid transformation is a transformation of the plane that preserves length.

Reflections, translations, rotations, and combinations of these three transformations are "rigid transformations".

The transformation $(x, y) \rightarrow (3x, y)$ is a transformation where the x-value of the original figure is streched by a factor of 3.


Therefore, the correct explanation is
The transformation is a stretch by a factor of 3, so it preserves the length of y segments but not the length of x segments. In order to be a rigid motion, the transformation must preserve lengths, so this transformation not a rigid motion.