Question

answer the question correctly to continue: what transformation combination would not result in similarity? a translation followed by a reflection. a reflection followed by a vertical stretch a dilation by a factor of 2. a rotation followed by a dilation.

Explanation:

Step1: Recall similarity transformation rules

Similarity transformations include translations, rotations, reflections (rigid motions) and dilations. Rigid motions preserve shape and size (so they make congruent - which is a special case of similar) and dilations preserve shape (scale size).

Step2: Analyze each option

• Option 1 (A translation followed by a reflection): Translation and reflection are rigid motions. Rigid motions result in congruent (and thus similar) figures.
• Option 2 (A reflection followed by a vertical stretch): A vertical stretch changes the shape (if it's not uniform scaling). Similarity requires that the ratio of corresponding side lengths is equal. A non - uniform stretch (vertical stretch without a corresponding horizontal stretch) will not preserve the ratio of side lengths for non - vertical/horizontal sides.
• Option 3 (A dilation by a factor of 2): Dilation is a similarity transformation as it scales the figure uniformly.
• Option 4 (A rotation followed by a dilation): Rotation (rigid motion) and dilation. The rigid motion preserves shape and size (for the first figure) and dilation scales it. Since the dilation is uniform, the figures are similar.

Answer:

A reflection followed by a vertical stretch.