Question

tanyas rotation maps point \\(k(24, -15)\\) to \\(k(-15, -24)\\). which describes the rotation?

\\(90^\circ\\) clockwise rotation
\\(270^\circ\\) clockwise rotation
\\(180^\circ\\) rotation
\\(90^\circ\\) counterclockwise rotation

Explanation:

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<reasoning>

Identify coordinates and mapping

\[
K(x, y) = K(24, -15)
ightarrow K'(x', y') = K'(-15, -24)
\]

Determine the transformation rule

\[
(x, y)
ightarrow (y, -x)
\]

Match rule to rotation description

\[
(x, y)
ightarrow (y, -x) \text{ represents a } 90^\circ \text{ clockwise rotation about the origin.}
\]
</reasoning>

<answer>
<mcq-correct>(A) 90° clockwise rotation</mcq-correct>
<mcq-option>(B) 270° clockwise rotation</mcq-option>
<mcq-option>(C) 180° rotation</mcq-option>
<mcq-option>(D) 90° counterclockwise rotation</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Rotation Rules"
]
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Answer:

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</pre_analysis>

<reasoning>

Identify coordinates and mapping

\[
K(x, y) = K(24, -15)
ightarrow K'(x', y') = K'(-15, -24)
\]

Determine the transformation rule

\[
(x, y)
ightarrow (y, -x)
\]

Match rule to rotation description

\[
(x, y)
ightarrow (y, -x) \text{ represents a } 90^\circ \text{ clockwise rotation about the origin.}
\]
</reasoning>

<answer>
<mcq-correct>(A) 90° clockwise rotation</mcq-correct>
<mcq-option>(B) 270° clockwise rotation</mcq-option>
<mcq-option>(C) 180° rotation</mcq-option>
<mcq-option>(D) 90° counterclockwise rotation</mcq-option>
</answer>

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"subject": "Mathematics",
"question_type": "Multiple Choice",
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"Mathematics",
"Geometry",
"Rotation Rules"
]
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