which rule represents the translation from the pre-image, $\delta abc$, to the image, $\delta abc$?

$(x, y) \
ightarrow (x + 7, y + 6)$
$(x, y) \
ightarrow (x + 7, y - 6)$
$(x, y) \
ightarrow (x - 6, y + 7)$
$(x, y) \
ightarrow (x + 6, y + 7)$

Question

which rule represents the translation from the pre-image, $\delta abc$, to the image, $\delta abc$?

$(x, y) \
ightarrow (x + 7, y + 6)$
$(x, y) \
ightarrow (x + 7, y - 6)$
$(x, y) \
ightarrow (x - 6, y + 7)$
$(x, y) \
ightarrow (x + 6, y + 7)$

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": [ "Coordinate Translations", "Geometric Transformations" ], "current_concepts": [ "Coordinate Translations", "Geometric Transformations" ] } ## Identify coordinates of pre-image and image vertices $$ \begin{aligned} &A = (-3, 4) \ &A' = (4, -2) \end{aligned} $$ ## Calculate horizontal and vertical shifts $$ \begin{aligned} &\Delta x = x_{A'} - x_A = 4 - (-3) = 7 \ &\Delta y = y_{A'} - y_A = -2 - 4 = -6 \end{aligned} $$ ## Determine translation rule $$ (x, y) ightarrow (x + 7, y - 6) $$

(A) $(x, y) ightarrow (x + 7, y + 6)$

(B) $(x, y) ightarrow (x + 7, y - 6)$

(C) $(x, y) ightarrow (x - 6, y + 7)$

(D) $(x, y) ightarrow (x + 6, y + 7)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Translations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coordinates of pre-image and image vertices

Calculate horizontal and vertical shifts

Determine translation rule

Answer: