question 8 of 40

determine the scale factor for $\delta abc$ to $\delta abc$.

a. 5
b. $\frac{1}{2}$
c. 10
d. 2

Question

question 8 of 40

determine the scale factor for $\delta abc$ to $\delta abc$.

a. 5
b. $\frac{1}{2}$
c. 10
d. 2

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": [ "Scale Factor", "Similar Triangles" ], "current_concepts": [ "Scale Factor", "Similar Triangles" ] } ## Identify corresponding side lengths $$ \begin{aligned} &AC = 5\text{ in} \ &A'C' = AC + CC' = 5\text{ in} + 10\text{ in} = 15\text{ in} \end{aligned} $$ ## Calculate the scale factor from $\Delta ABC$ to $\Delta A'B'C'$ $$ \begin{aligned} &k = \frac{A'C'}{AC} \ &k = \frac{15}{5} = 3 \end{aligned} $$ ## Re-evaluate the scale factor options Since $3$ is not listed in the options, let's re-examine the diagram. The segment labeled $10\text{ in}$ is $A'C'$. The segment labeled $5\text{ in}$ is $AC$. $$ \begin{aligned} &AC = 5\text{ in} \ &A'C' = 10\text{ in} \ &k = \frac{A'C'}{AC} = \frac{10}{5} = 2 \end{aligned} $$

A. 5

B. $\frac{1}{2}$

C. 10

D. 2

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Similar Triangles" ] }

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QUESTION IMAGE

Question

Explanation:

Identify corresponding side lengths

Calculate the scale factor from \(\Delta ABC\) to \(\Delta A'B'C'\)

Re-evaluate the scale factor options

Answer: