A sequence of transformations that results in a figure being similar to the original figure must include a dilation. Rotations, reflections, and translations alone will not change the size, and thus create congruent figures. Only the sequences including dilation with a scale factor other than 1 will produce similar, but not congruent, figures.
The sequence of transformations that would result in a figure that is similar, but not congruent, to the original figure must include a dilation.
Transformations such as rotations, reflections, and translations will preserve the shape and size, leading to congruent figures.
However, dilation changes the size while maintaining the shape, achieving similarity without congruence.
- A rotation about the origin of 50° followed by a dilation with a scale factor of 8 will result in a similar figure, as the dilation alters the size.
- A reflection across the y-axis followed by a rotation about the origin of 10° will only produce a congruent figure, since these transformations don't change the size.
- A dilation with a scale factor of 0.6 followed by a translation of 2 units up also results in a similar figure, because dilation changes the size while the translation just moves the figure.
- A translation 2 units up followed by a translation of 2 units to the left does not change the size of the figure, hence it will be congruent to the original figure, not similar.