Question

find the distance between each pair of points. leave your answer in square root form. type your answer in the form sqrt(...)

distance =

Explanation:

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<reasoning>

Identify the coordinates of the endpoints from the graph

\[

$$\begin{aligned} &(x_1, y_1) = (2, 3)\\ &(x_2, y_2) = (4, -3) \end{aligned}$$

\]

Apply the distance formula

\[

$$\begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\ d &= \sqrt{(4 - 2)^2 + (-3 - 3)^2}\\ d &= \sqrt{2^2 + (-6)^2}\\ d &= \sqrt{4 + 36}\\ d &= \sqrt{40} \end{aligned}$$

\]

Simplify the radical expression

\[

$$\begin{aligned} d &= \sqrt{4 \times 10}\\ d &= 2\sqrt{10} \end{aligned}$$

\]
</reasoning>

<answer>
Find the distance between each pair of points. Leave your answer in square root form. Type your answer in the form sqrt(...) with no spaces.

Distance = <blank>sqrt(40)</blank>
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
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"Mathematics",
"Geometry",
"Distance Formula"
]
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Answer:

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<reasoning>

Identify the coordinates of the endpoints from the graph

\[

$$\begin{aligned} &(x_1, y_1) = (2, 3)\\ &(x_2, y_2) = (4, -3) \end{aligned}$$

\]

Apply the distance formula

\[

$$\begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\ d &= \sqrt{(4 - 2)^2 + (-3 - 3)^2}\\ d &= \sqrt{2^2 + (-6)^2}\\ d &= \sqrt{4 + 36}\\ d &= \sqrt{40} \end{aligned}$$

\]

Simplify the radical expression

\[

$$\begin{aligned} d &= \sqrt{4 \times 10}\\ d &= 2\sqrt{10} \end{aligned}$$

\]
</reasoning>

<answer>
Find the distance between each pair of points. Leave your answer in square root form. Type your answer in the form sqrt(...) with no spaces.

Distance = <blank>sqrt(40)</blank>
</answer>

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