29. Which of the following transformations will result in a similar but not congruent figure?
Answer: C
Dilation results in a similar but not congruent figure.
Dilation is a transformation that alters the size of a figure while maintaining its shape, leading to a similar figure that is not congruent to the original. This means that while the two figures share the same proportions, their sizes differ.
A) Reflection
Reflection produces a mirror image of the original figure, maintaining both size and shape, making the two figures congruent. Therefore, reflection does not create a similar figure that is not congruent.
B) Translation
Translation moves a figure from one location to another without altering its size or shape. This transformation results in two congruent figures, not a similar figure that differs in size.
C) Dilation
Dilation changes the size of a figure by a scale factor, leading to a similar figure that retains the same shape but is different in size. This makes dilation the correct transformation for producing a similar but not congruent figure.
D) Rotation
Rotation turns a figure around a fixed point without changing its size or shape. Like reflection and translation, rotation results in congruent figures, thus not fulfilling the requirement of creating a similar but not congruent figure.
Conclusion
Dilation is the only transformation among the options that results in a similar figure that is not congruent to the original. All other transformations—reflection, translation, and rotation—preserve the size and shape of the figure, resulting in congruent figures instead. Thus, dilation is definitively the correct choice for this question.