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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Coordinate Transformations" ], "new_concepts": [ "Rotational Transformations" ], "current_concepts": [ "Coordinate Transformations", "Rotational Transformations" ] } ## Identify the transformation rule $$ R_{0, 90^\circ}(x, y) = (-y, x) $$ ## Set up the equation for the image point $$ \begin{aligned} &Q'(x', y') = (-3, 4) \ &(-y, x) = (-3, 4) \end{aligned} $$ ## Solve for the original coordinates $$ \begin{aligned} &-y = -3 \implies y = 3 \ &x = 4 \ &Q(x, y) = (4, 3) \end{aligned} $$

(A) $(-4, -3)$

(B) $(-3, -4)$

(C) $(3, 4)$

(D) $(4, 3)$

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

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Explanation:

Identify the transformation rule

Set up the equation for the image point

Solve for the original coordinates

Answer: