Question

marissa wants to write an abbreviated set of directions for finding coordinates of a figure reflected across the \\(y\\)-axis. which mapping notation is correct?

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

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Coordinate Transformations",
"Reflection Across Axes"
],
"new_concepts": [],
"current_concepts": [
"Coordinate Transformations",
"Reflection Across Axes"
]
}
</pre_analysis>

<reasoning>

Identify the transformation rule

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

Verify the reflection across the y-axis

\[

$$\begin{aligned} &\text{Reflection across } y\text{-axis changes the sign of the } x\text{-coordinate.}\\ &\text{The } y\text{-coordinate remains unchanged.}\\ &(x, y) ightarrow (-x, y) \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \((x,y)
ightarrow (-x,y)\)</mcq-correct>
<mcq-option>(B) \((x,y)
ightarrow (x,-y)\)</mcq-option>
<mcq-option>(C) \((x,y)
ightarrow (-x,-y)\)</mcq-option>
<mcq-option>(D) \((x,y)
ightarrow (y,x)\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Reflection Across Axes"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Coordinate Transformations",
"Reflection Across Axes"
],
"new_concepts": [],
"current_concepts": [
"Coordinate Transformations",
"Reflection Across Axes"
]
}
</pre_analysis>

<reasoning>

Identify the transformation rule

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

Verify the reflection across the y-axis

\[

$$\begin{aligned} &\text{Reflection across } y\text{-axis changes the sign of the } x\text{-coordinate.}\\ &\text{The } y\text{-coordinate remains unchanged.}\\ &(x, y) ightarrow (-x, y) \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \((x,y)
ightarrow (-x,y)\)</mcq-correct>
<mcq-option>(B) \((x,y)
ightarrow (x,-y)\)</mcq-option>
<mcq-option>(C) \((x,y)
ightarrow (-x,-y)\)</mcq-option>
<mcq-option>(D) \((x,y)
ightarrow (y,x)\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Reflection Across Axes"
]
}
</post_analysis>