Question

andrews rotation maps point \\(m(9, -1)\\) to \\(m(-9, 1)\\). which describes the rotation?

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

Explanation:

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<reasoning>

Identify the coordinates of the pre-image and image

Using the Rotation Rules knowledge point
\[
M(x, y) = M(9, -1)
\]
\[
M'(x', y') = M'(-9, 1)
\]

Determine the coordinate transformation rule

Using the Rotation Rules knowledge point
\[
(x, y)
ightarrow (-x, -y)
\]

Identify the rotation corresponding to the rule

Using the Rotation Rules knowledge point
\[
R_{180^\circ}(x, y) = (-x, -y)
\]
</reasoning>

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

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Answer:

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<reasoning>

Identify the coordinates of the pre-image and image

Using the Rotation Rules knowledge point
\[
M(x, y) = M(9, -1)
\]
\[
M'(x', y') = M'(-9, 1)
\]

Determine the coordinate transformation rule

Using the Rotation Rules knowledge point
\[
(x, y)
ightarrow (-x, -y)
\]

Identify the rotation corresponding to the rule

Using the Rotation Rules knowledge point
\[
R_{180^\circ}(x, y) = (-x, -y)
\]
</reasoning>

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

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