which composition of similarity transformations maps $\delta lmn$ to $\delta lmn$?

a dilation with a scale factor less than 1 and then a reflection
a dilation with a scale factor less than 1 and then a translation
a dilation with a scale factor greater than 1 and then a reflection
a dilation with a scale factor greater than 1 and then a translation

Question

which composition of similarity transformations maps $\delta lmn$ to $\delta lmn$?

a dilation with a scale factor less than 1 and then a reflection
a dilation with a scale factor less than 1 and then a translation
a dilation with a scale factor greater than 1 and then a reflection
a dilation with a scale factor greater than 1 and then a translation

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Similarity Transformations", "Geometric Dilation", "Geometric Reflection" ], "current_concepts": [ "Similarity Transformations", "Geometric Dilation", "Geometric Reflection" ] } ## Determine the scale factor of the dilation $$ \begin{aligned} &LN = 2,\quad L'N' = 4\ &k = \frac{L'N'}{LN} = \frac{4}{2} = 2 > 1 \end{aligned} $$ ## Identify the second transformation $$ \begin{aligned} &\text{Orientation of }\Delta LMN\text{ is counterclockwise: } L(-1,3) \to M(3,1) \to N(-1,1)\ &\text{Orientation of }\Delta L'M'N'\text{ is clockwise: } L'(-2,-1) \to M'(6,-5) \to N'(-2,-5)\ &\text{A change in orientation indicates a reflection.} \end{aligned} $$

a dilation with a scale factor less than 1 and then a reflection

a dilation with a scale factor less than 1 and then a translation

a dilation with a scale factor greater than 1 and then a reflection

a dilation with a scale factor greater than 1 and then a translation

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Similarity Transformations" ] }

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Question

Explanation:

Determine the scale factor of the dilation

Identify the second transformation

Answer: