Question

the midpoint of a line segment partitions the line segment into a ratio of

1:1
1:2
2:1
2:3

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Directed Line Segments",
"Section Formula"
],
"new_concepts": [
"Midpoint Partition Ratio"
],
"current_concepts": [
"Directed Line Segments",
"Section Formula",
"Midpoint Partition Ratio"
]
}
</pre_analysis>

<reasoning>

Define midpoint partition

\[
AP = PB
\]

Calculate the ratio

\[
\text{Ratio} = \frac{AP}{PB} = \frac{1}{1} = 1:1
\]
</reasoning>

<answer>
<mcq-correct>(A) 1:1.</mcq-correct>
<mcq-option>(B) 1:2.</mcq-option>
<mcq-option>(C) 2:1.</mcq-option>
<mcq-option>(D) 2:3.</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Directed Line Segments"
]
}
</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": [
"Directed Line Segments",
"Section Formula"
],
"new_concepts": [
"Midpoint Partition Ratio"
],
"current_concepts": [
"Directed Line Segments",
"Section Formula",
"Midpoint Partition Ratio"
]
}
</pre_analysis>

<reasoning>

Define midpoint partition

\[
AP = PB
\]

Calculate the ratio

\[
\text{Ratio} = \frac{AP}{PB} = \frac{1}{1} = 1:1
\]
</reasoning>

<answer>
<mcq-correct>(A) 1:1.</mcq-correct>
<mcq-option>(B) 1:2.</mcq-option>
<mcq-option>(C) 2:1.</mcq-option>
<mcq-option>(D) 2:3.</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Directed Line Segments"
]
}
</post_analysis>