Question

find the distance between the points.

\\((-3, -4)\\) and \\((-3, -1)\\)

the distance is \\(\square\\).

Explanation:

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<reasoning>

Identify the coordinates of the given points

\[
(x_1, y_1) = (-3, -4),\quad (x_2, y_2) = (-3, -1)
\]

Apply the vertical distance formula

\[

$$\begin{aligned} d &= |y_2 - y_1| \\ &= |-1 - (-4)| \\ &= |-1 + 4| \\ &= |3| \\ &= 3 \end{aligned}$$

\]
</reasoning>

<answer>
Find the distance between the points.

\( (-3, -4) \) and \( (-3, -1) \)

The distance is <blank>3</blank>.
</answer>

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"question_type": "Fill-in-the-blank",
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"Mathematics",
"Geometry",
"Coordinate Distance"
]
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Answer:

<pre_analysis>
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</pre_analysis>

<reasoning>

Identify the coordinates of the given points

\[
(x_1, y_1) = (-3, -4),\quad (x_2, y_2) = (-3, -1)
\]

Apply the vertical distance formula

\[

$$\begin{aligned} d &= |y_2 - y_1| \\ &= |-1 - (-4)| \\ &= |-1 + 4| \\ &= |3| \\ &= 3 \end{aligned}$$

\]
</reasoning>

<answer>
Find the distance between the points.

\( (-3, -4) \) and \( (-3, -1) \)

The distance is <blank>3</blank>.
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Coordinate Distance"
]
}
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