Question

find the distance between the pair of points.

\\((12,23)\\) and \\((-3,-10)\\)

the distance is \\(\square\\).
(round to the nearest thousandth as needed.)

Explanation:

<pre_analysis>
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<reasoning>

Identify the given coordinates

Using the Coordinate Distance knowledge point
\[
(x_1, y_1) = (12, 23)
\]
\[
(x_2, y_2) = (-3, -10)
\]

Apply the distance formula

Using the Distance Formula knowledge point
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
\[
d = \sqrt{(-3 - 12)^2 + (-10 - 23)^2}
\]

Simplify the differences

Using the Distance Formula knowledge point
\[
d = \sqrt{(-15)^2 + (-33)^2}
\]
\[
d = \sqrt{225 + 1089}
\]

Calculate the final distance

Using the Distance Formula knowledge point
\[
d = \sqrt{1314} \approx 36.2491379
\]
\[
d \approx 36.249
\]
</reasoning>

<answer>
Find the distance between the pair of points.

\((12,23)\) and \((-3,-10)\)

The distance is <blank>36.249</blank>.
(Round to the nearest thousandth as needed.)
</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Distance Formula"
]
}
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Answer:

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"step_cot",
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"concepts_used": [
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"new_concepts": [],
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</pre_analysis>

<reasoning>

Identify the given coordinates

Using the Coordinate Distance knowledge point
\[
(x_1, y_1) = (12, 23)
\]
\[
(x_2, y_2) = (-3, -10)
\]

Apply the distance formula

Using the Distance Formula knowledge point
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
\[
d = \sqrt{(-3 - 12)^2 + (-10 - 23)^2}
\]

Simplify the differences

Using the Distance Formula knowledge point
\[
d = \sqrt{(-15)^2 + (-33)^2}
\]
\[
d = \sqrt{225 + 1089}
\]

Calculate the final distance

Using the Distance Formula knowledge point
\[
d = \sqrt{1314} \approx 36.2491379
\]
\[
d \approx 36.249
\]
</reasoning>

<answer>
Find the distance between the pair of points.

\((12,23)\) and \((-3,-10)\)

The distance is <blank>36.249</blank>.
(Round to the nearest thousandth as needed.)
</answer>

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