Question

if the product of two slopes is ________, then the two lines are perpendicular.

• 0
• -1

Explanation:

<pre_analysis>
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"concepts_used": [
"Parallel and Perpendicular Lines"
],
"new_concepts": [],
"current_concepts": [
"Parallel and Perpendicular Lines",
"Slope of a Linear Function"
]
}
</pre_analysis>

<reasoning>

Identify the geometric condition for perpendicular lines

\[
m_1 \cdot m_2 = -1
\]

Match with the given options

\[
\text{Product} = -1
\]
</reasoning>

<answer>
<mcq-option>0</mcq-option>
<mcq-correct>-1</mcq-correct>
</answer>

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

Answer:

<pre_analysis>
{
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"step_cot",
"multiple_choice_formatter",
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"Parallel and Perpendicular Lines"
],
"new_concepts": [],
"current_concepts": [
"Parallel and Perpendicular Lines",
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</pre_analysis>

<reasoning>

Identify the geometric condition for perpendicular lines

\[
m_1 \cdot m_2 = -1
\]

Match with the given options

\[
\text{Product} = -1
\]
</reasoning>

<answer>
<mcq-option>0</mcq-option>
<mcq-correct>-1</mcq-correct>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Parallel and Perpendicular Lines"
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