Which composition of similarity transformations maps polygon ABCD to polygon A'B'C'D?

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A. Reflection followed by a translation

B. Dilation followed by rotation

C. Translation followed by reflection

D. Rotation followed by reflection

Correct Answer:

Dilation followed by rotation

Why Not the Other Options?

• Option A: Reflection and translation can change a figure’s position and orientation but do not maintain similarity unless a dilation is involved.
• Option C: A translation and reflection can create congruence but not similarity since similarity requires proportional scaling.
• Option D: Rotation and reflection can change orientation but do not change the size proportionally.

Properties of Similar Figures:

• Corresponding angles are always congruent.
• The corresponding sides are proportional (same ratio).
• Orientation may or may not be preserved depending on the type of transformation used.

FAQs About Similarity Transformations

What is a similarity transformation in geometry?

A similarity transformation in geometry is a process where combining the varied transformations (dilation, reflection, rotation, and translation) gives a figure similar to the original one. It preserves the shape of the figure but not its size.

How does dilation affect a polygon?

Dilation affects the size of a polygon. If it increases the size of the polygon it's considered an enlargement and if it reduces it, it's called a reduction. Though it leaves the angles and the proportional relationship as they were.

Why is a dilation followed by a rotation considered a similarity transformation?

A dilation changes only the size of the figure while the rotation preserves the shape and size of the figure. When a rotation follows the dilation, the result will have the same shape but a different size. This similarity with the original figure makes a similar transformation.

What is the difference between similarity and congruence?

• Similarity: Figures have the same shape but different sizes.
• Congruence: Figures have the same shape and size.

How do you identify the scale factor in a dilation?

Dilation changes the figure size without actually affecting its shape or its intrinsic properties like angle. This makes it important for similarity transformations.

Can multiple similarity transformations be applied to the same figure?

Yes, you can indeed apply multiple similarity transformations to the same figure. Reflection or rotation can be applied to a figure after dilation and still get a similar figure.