Question

drag each variable to the correct location on the ordered pair. not all variables will be used.

triangle \\(abc\\) is reflected across the \\(y\\)-axis to create triangle \\(abc\\). complete the ordered pair to describe this transformation.

\\((x, y) = (\quad, \quad)\\)

options:
\\(-x\\), \\(x\\), \\(y\\), \\(-y\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Geometric Transformations",
"Reflection Rule",
"y-axis Reflection"
],
"new_concepts": [],
"current_concepts": [
"Geometric Transformations",
"Reflection Rule",
"y-axis Reflection"
]
}
</pre_analysis>

<reasoning>

Identify the transformation rule

The problem states that Triangle \(ABC\) is reflected across the \(y\)-axis to create triangle \(A'B'C'\).

Apply the reflection rule

A reflection of a point \((x, y)\) across the \(y\)-axis negates the \(x\)-coordinate while keeping the \(y\)-coordinate unchanged:
\[
(x', y') = (-x, y)
\]
</reasoning>

<answer>
Triangle ABC is reflected across the \(y\)-axis to create triangle \(A'B'C'\). Complete the ordered pair to describe this transformation.

\((x', y') =\) (<blank>\(-x\)</blank>, <blank>\(y\)</blank>)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Geometric Transformations"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Geometric Transformations",
"Reflection Rule",
"y-axis Reflection"
],
"new_concepts": [],
"current_concepts": [
"Geometric Transformations",
"Reflection Rule",
"y-axis Reflection"
]
}
</pre_analysis>

<reasoning>

Identify the transformation rule

The problem states that Triangle \(ABC\) is reflected across the \(y\)-axis to create triangle \(A'B'C'\).

Apply the reflection rule

A reflection of a point \((x, y)\) across the \(y\)-axis negates the \(x\)-coordinate while keeping the \(y\)-coordinate unchanged:
\[
(x', y') = (-x, y)
\]
</reasoning>

<answer>
Triangle ABC is reflected across the \(y\)-axis to create triangle \(A'B'C'\). Complete the ordered pair to describe this transformation.

\((x', y') =\) (<blank>\(-x\)</blank>, <blank>\(y\)</blank>)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Geometric Transformations"
]
}
</post_analysis>