Question

سوال ۸ از ۱۵ زمان پیشنهادی: ۶۰ دقیقه

جاهای خالی به ترتیب با کدام یک از گزینه ها پر می شود.
خط \\(y=3\\) موازی محور .......... است و زاویه آن با محور طول ها .......... است.

پاسخ دانش آموز

عرض ها - ۹۰ درجه

طولها - ۹۰ درجه

عرض ها - صفر درجه

طولها - صفر درجه

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": true,
"concepts_used": [],
"new_concepts": [
"Horizontal Lines",
"Coordinate Axes",
"Angle of Inclination"
],
"current_concepts": [
"Horizontal Lines",
"Coordinate Axes",
"Angle of Inclination"
]
}
</pre_analysis>

<reasoning>

Translate and analyze the question

The Persian text translates to:
"Which of the options fills the blanks in order?
The line \(y = 3\) is parallel to the .......... axis and its angle with the axis of abscissas (x-axis) is .......... ."

Determine the parallel axis

The equation \(y = 3\) represents a horizontal line.
A horizontal line is parallel to the x-axis (axis of abscissas / "محور طول‌ها").
In Persian:

• "طول‌ها" means abscissas (x-axis).
• "عرض‌ها" means ordinates (y-axis).

Therefore, the line \(y = 3\) is parallel to the x-axis ("محور طول‌ها").

Determine the angle with the x-axis

Since the line \(y = 3\) is parallel to the x-axis, the angle between them is \(0^\circ\) ("صفر درجه").

Match with the options

The correct sequence to fill the blanks is:

1. "طول‌ها" (abscissas / x-axis)
2. "صفر درجه" (zero degrees)

This corresponds to the fourth option: "طول‌ها - صفر درجه".
</reasoning>

<answer>
<mcq-option>(A) عرض‌ها - ۹۰ درجه (y-axis - 90 degrees)</mcq-option>
<mcq-option>(B) طول‌ها - ۹۰ درجه (x-axis - 90 degrees)</mcq-option>
<mcq-option>(C) عرض‌ها - صفر درجه (y-axis - 0 degrees)</mcq-option>
<mcq-correct>(D) طول‌ها - صفر درجه (x-axis - 0 degrees)</mcq-correct>
</answer>

<plot>
{
"elements": [
{
"type": "line",
"params": [[-10, 0], [10, 0]],
"properties": {
"name": "x-axis",
"strokeColor": "#583C87",
"strokeWidth": 2,
"withLabel": true,
"labelPosition": [8, 0.5]
}
},
{
"type": "line",
"params": [[0, -10], [0, 10]],
"properties": {
"name": "y-axis",
"strokeColor": "#583C87",
"strokeWidth": 2,
"withLabel": true,
"labelPosition": [0.5, 8]
}
},
{
"type": "line",
"params": [[-10, 3], [10, 3]],
"properties": {
"name": "y = 3",
"strokeColor": "#8C55F2",
"strokeWidth": 3,
"withLabel": true,
"labelPosition": [6, 3.5]
}
}
],
"timestamps": [0.5]
}
</plot>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Horizontal Lines"
]
}
</post_analysis>

Answer:

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"question_count": 1,
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"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": true,
"concepts_used": [],
"new_concepts": [
"Horizontal Lines",
"Coordinate Axes",
"Angle of Inclination"
],
"current_concepts": [
"Horizontal Lines",
"Coordinate Axes",
"Angle of Inclination"
]
}
</pre_analysis>

<reasoning>

Translate and analyze the question

The Persian text translates to:
"Which of the options fills the blanks in order?
The line \(y = 3\) is parallel to the .......... axis and its angle with the axis of abscissas (x-axis) is .......... ."

Determine the parallel axis

The equation \(y = 3\) represents a horizontal line.
A horizontal line is parallel to the x-axis (axis of abscissas / "محور طول‌ها").
In Persian:

• "طول‌ها" means abscissas (x-axis).
• "عرض‌ها" means ordinates (y-axis).

Therefore, the line \(y = 3\) is parallel to the x-axis ("محور طول‌ها").

Determine the angle with the x-axis

Since the line \(y = 3\) is parallel to the x-axis, the angle between them is \(0^\circ\) ("صفر درجه").

Match with the options

The correct sequence to fill the blanks is:

1. "طول‌ها" (abscissas / x-axis)
2. "صفر درجه" (zero degrees)

This corresponds to the fourth option: "طول‌ها - صفر درجه".
</reasoning>

<answer>
<mcq-option>(A) عرض‌ها - ۹۰ درجه (y-axis - 90 degrees)</mcq-option>
<mcq-option>(B) طول‌ها - ۹۰ درجه (x-axis - 90 degrees)</mcq-option>
<mcq-option>(C) عرض‌ها - صفر درجه (y-axis - 0 degrees)</mcq-option>
<mcq-correct>(D) طول‌ها - صفر درجه (x-axis - 0 degrees)</mcq-correct>
</answer>

<plot>
{
"elements": [
{
"type": "line",
"params": [[-10, 0], [10, 0]],
"properties": {
"name": "x-axis",
"strokeColor": "#583C87",
"strokeWidth": 2,
"withLabel": true,
"labelPosition": [8, 0.5]
}
},
{
"type": "line",
"params": [[0, -10], [0, 10]],
"properties": {
"name": "y-axis",
"strokeColor": "#583C87",
"strokeWidth": 2,
"withLabel": true,
"labelPosition": [0.5, 8]
}
},
{
"type": "line",
"params": [[-10, 3], [10, 3]],
"properties": {
"name": "y = 3",
"strokeColor": "#8C55F2",
"strokeWidth": 3,
"withLabel": true,
"labelPosition": [6, 3.5]
}
}
],
"timestamps": [0.5]
}
</plot>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Horizontal Lines"
]
}
</post_analysis>