in the similarity transformation of $\delta abc$ to $\delta fed$, $\delta abc$ was dilated by a scale factor of $\frac{1}{2}$, reflected across the $y$-axis, and moved through the translation ? .

* $(x+1, y+1)$
* $(x+2, y-1)$
* $(x+0, y+1)$
* $(x+1, y-1)$

Question

in the similarity transformation of $\delta abc$ to $\delta fed$, $\delta abc$ was dilated by a scale factor of $\frac{1}{2}$, reflected across the $y$-axis, and moved through the translation  ? .

* $(x+1, y+1)$
* $(x+2, y-1)$
* $(x+0, y+1)$
* $(x+1, y-1)$

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": [ "Coordinate Dilation", "Coordinate Reflection", "Coordinate Translation", "Composite Transformations" ], "new_concepts": [], "current_concepts": [ "Coordinate Dilation", "Coordinate Reflection", "Coordinate Translation", "Composite Transformations", "Similarity Transformations" ] } ## Identify original coordinates Find coordinates of $\triangle ABC$ from the graph. $$ A = (-8, 2),\quad B = (-4, 4),\quad C = (-2, 2) $$ ## Apply coordinate dilation Using the **Coordinate Dilation** knowledge point $$ \begin{aligned} &k = \frac{1}{2}\ &A' = (-4, 1),\quad B' = (-2, 2),\quad C' = (-1, 1) \end{aligned} $$ ## Apply coordinate reflection Using the **Coordinate Reflection** knowledge point $$ \begin{aligned} &(x, y) \to (-x, y)\ &A'' = (4, 1),\quad B'' = (2, 2),\quad C'' = (1, 1) \end{aligned} $$ ## Determine coordinate translation Using the **Coordinate Translation** and **Composite Transformations** knowledge points $$ \begin{aligned} &F = (5, 0),\quad E = (3, 1),\quad D = (2, 0)\ &A'' \to F \implies (4 + a, 1 + b) = (5, 0) \implies a = 1, b = -1\ &B'' \to E \implies (2 + a, 2 + b) = (3, 1) \implies a = 1, b = -1\ &C'' \to D \implies (1 + a, 1 + b) = (2, 0) \implies a = 1, b = -1\ &(x, y) \to (x + 1, y - 1) \end{aligned} $$

(A) $(x+1, y+1)$

(B) $(x+2, y-1)$

(C) $(x+0, y+1)$

(D) $(x+1, y-1)$

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

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QUESTION IMAGE

Question

Explanation:

Identify original coordinates

Apply coordinate dilation

Apply coordinate reflection

Determine coordinate translation

Answer: