Question

question 5 of 5

type the correct answer in the box.

triangle \\(qrs\\) is reflected across the \\(y\\)-axis to create triangle \\(qrs\\). complete the rule that describes the coordinates of triangle \\(qrs\\) after the reflection has occurred.

\\(x, y\\)

Explanation:

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

<reasoning>

Identify the transformation type

The problem states that triangle \(QRS\) is reflected across the \(y\)-axis to create triangle \(Q'R'S'\).

Apply the reflection rule

A reflection across the \(y\)-axis negates the \(x\)-coordinate of each point while keeping the \(y\)-coordinate the same:
\[
(x, y)
ightarrow (-x, y)
\]

Determine the coordinates of the image

The coordinates of the reflected points \(x'\) and \(y'\) are given by:
\[
x' = -x,\quad y' = y
\]
Thus, the rule describing the coordinates is \((-x, y)\).
</reasoning>

<answer>
Triangle \(QRS\) is reflected across the \(y\)-axis to create triangle \(Q'R'S'\). Complete the rule that describes the coordinates of triangle \(Q'R'S'\) after the reflection has occurred.

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

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

Answer:

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

<reasoning>

Identify the transformation type

The problem states that triangle \(QRS\) is reflected across the \(y\)-axis to create triangle \(Q'R'S'\).

Apply the reflection rule

A reflection across the \(y\)-axis negates the \(x\)-coordinate of each point while keeping the \(y\)-coordinate the same:
\[
(x, y)
ightarrow (-x, y)
\]

Determine the coordinates of the image

The coordinates of the reflected points \(x'\) and \(y'\) are given by:
\[
x' = -x,\quad y' = y
\]
Thus, the rule describing the coordinates is \((-x, y)\).
</reasoning>

<answer>
Triangle \(QRS\) is reflected across the \(y\)-axis to create triangle \(Q'R'S'\). Complete the rule that describes the coordinates of triangle \(Q'R'S'\) after the reflection has occurred.

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

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