https://file.aiquickdraw.com/mathbot/file/1726533778234r2i8cefo.jpg

To find the distance between points \( A \) and \( B \) in the image, we will apply the distance formula, which is:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

From the image, we can determine the coordinates of points \( A \) and \( B \):
- \( A \) appears to be located at approximately (-8, -2).
- \( B \) appears to be located at approximately (4, 6).

Now, using these coordinates in the distance formula:
\[
d = \sqrt{(4 - (-8))^2 + (6 - (-2))^2}
\]
\[
d = \sqrt{(4 + 8)^2 + (6 + 2)^2}
\]
\[
d = \sqrt{12^2 + 8^2}
\]
\[
d = \sqrt{144 + 64}
\]
\[
d = \sqrt{208} \approx 14.42
\]

So, the distance between \( A \) and \( B \) is approximately **14.42 units**.

Would you like more details on this solution or further clarification?

Here are 5 related questions to deepen your understanding:
1. How is the distance formula derived from the Pythagorean theorem?
2. How would the formula change if we were working in 3D space?
3. Can the distance formula be used to find the length of curves in a graph?
4. What is the significance of negative coordinates in the distance formula?
5. How would rounding to a different number of decimal places affect the answer?

**Tip:** Always double-check the coordinates from the graph to ensure accuracy when calculating distances.

Find the distance between A and B. Round your answer to two decimal places.

Learn how to calculate the distance between two points, A(-8, -2) and B(4, 6), on a coordinate plane using the distance formula. This detailed guide walks through the steps of using the formula sqrt((x2 - x1)^2 + (y2 - y1)^2), resulting in a final distance of approximately 14.42 units. Suitable for high school students.

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