Question

identifying a sequence of similarity transformations
triangle abc is similar to triangle abc.
which sequence of similar transformations could map △abc onto △abc?
options:
dilation and translation
translation and rotation
translation and reflection
dilation and reflection

Explanation:

Step1: Analyze Similarity Transformations

Similarity transformations include dilation (resizing), translation (moving), rotation (turning), and reflection (flipping). For similar triangles, dilation changes size, and other transformations change position/orientation. Here, $\triangle ABC$ and $\triangle A'B'C'$ have different sizes (so dilation is needed) and can be moved (translation) to align. Rotation/reflection would change orientation, but angles match, so dilation (to resize) and translation (to move) make sense.

Step2: Evaluate Options

• "translation and rotation": No size change, so wrong.
• "translation and reflection": No size change, wrong.
• "dilation and reflection": Reflection not needed (angles same orientation).
• "dilation and translation": Dilation resizes $\triangle ABC$ to match $\triangle A'B'C'$'s size, translation moves it to position. This fits.

Answer:

dilation and translation