a \approx 5.8
\approx 5.8
\approx 3.6
\approx 3.2
p
6
c
b
\approx 4.1

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Transformations", "Dilation Scale Factor", "Center of Dilation" ], "new_concepts": [], "current_concepts": [ "Geometric Transformations", "Dilation Scale Factor", "Center of Dilation" ] } ## Identify corresponding side lengths of the original and dilated triangles $$ \begin{aligned} &\text{Original side } AB \approx 3.2 \ &\text{Dilated side } A'B' \approx 5.8 \ &\text{Original side } AC \approx 3.6 \ &\text{Dilated side } A'C' \approx 5.8 \ &\text{Original side } BC \approx 4.1 \ &\text{Dilated side } B'C' \approx 6.0 \end{aligned} $$ ## Calculate the scale factor $k$ using corresponding sides $$ \begin{aligned} &k = \frac{\text{Dilated side length}}{\text{Original side length}} \ &k_1 = \frac{5.8}{3.2} \approx 1.81 \ &k_2 = \frac{5.8}{3.6} \approx 1.61 \ &k_3 = \frac{6.0}{4.1} \approx 1.46 \end{aligned} $$ ## Determine the scale factor from grid coordinates $$ \begin{aligned} &\text{Let } P = (0, 0) \ &\text{Original vertex } C = (3, 0) \ &\text{Dilated vertex } C' = (5, 0) \ &k = \frac{x_{C'}}{x_C} = \frac{5}{3} \approx 1.67 \end{aligned} $$ The scale factor of the dilation is $\frac{5}{3}$ (or approximately $1.67$). { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Dilation Scale Factor" ] }

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Question

Explanation:

Identify corresponding side lengths of the original and dilated triangles

Calculate the scale factor \(k\) using corresponding sides

Determine the scale factor from grid coordinates

Answer: