in the similarity transformation of $\delta acb$ to $\delta efd$, $\delta acb$ was dilated by a scale factor of ? , reflected across the , and moved through the translation .

3
2
1/3
1/2

Question

in the similarity transformation of $\delta acb$ to $\delta efd$, $\delta acb$ was dilated by a scale factor of  ? , reflected across the  , and moved through the translation  .

3
2
1/3
1/2

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Scale Factor", "Coordinate Dilation" ], "new_concepts": [ "Similarity Transformations" ], "current_concepts": [ "Scale Factor", "Coordinate Dilation", "Similarity Transformations" ] } ## Identify corresponding vertices and coordinates Using the **Coordinate Dilation** knowledge point $$ \begin{aligned} &A(-1, 0), \quad C(-2, 2), \quad B(0, 1)\ &E(5, -1), \quad F(7, 3), \quad D(3, 1) \end{aligned} $$ ## Calculate side lengths of both triangles Using the **Scale Factor** knowledge point $$ \begin{aligned} &AC = \sqrt{(-2 - (-1))^2 + (2 - 0)^2} = \sqrt{1 + 4} = \sqrt{5}\ &EF = \sqrt{(7 - 5)^2 + (3 - (-1))^2} = \sqrt{4 + 16} = \sqrt{20} = 2\sqrt{5} \end{aligned} $$ ## Determine the scale factor of dilation Using the **Scale Factor** knowledge point $$ k = \frac{EF}{AC} = \frac{2\sqrt{5}}{\sqrt{5}} = 2 $$

3

2

1/3

1/2

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify corresponding vertices and coordinates

Calculate side lengths of both triangles

Determine the scale factor of dilation

Answer: