https://file.aiquickdraw.com/mathbot/file/1728581383774u63yt2nw.jpg

To find the distance between the two points shown on the graph, we can use the **distance formula**:

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

From the graph, the coordinates of the two points are approximately:
- Point 1: \((-4, 4)\)
- Point 2: \((2, -2)\)

Now we substitute these into the distance formula:

\[
d = \sqrt{(2 - (-4))^2 + (-2 - 4)^2}
\]
\[
d = \sqrt{(2 + 4)^2 + (-2 - 4)^2}
\]
\[
d = \sqrt{6^2 + (-6)^2}
\]
\[
d = \sqrt{36 + 36} = \sqrt{72}
\]

Now, find the square root of 72:

\[
d \approx 8.5
\]

Thus, the distance between the two points is approximately **8.5 units**.

Would you like further details, or do you have any questions?

Here are 5 related questions to explore:
1. How would the distance formula change if the points were in 3D space?
2. Can you explain why the distance formula works using the Pythagorean Theorem?
3. What are other methods to calculate distances between points?
4. How does rounding affect the accuracy of distance calculations?
5. How would you apply the distance formula in real-world contexts?

**Tip:** Always double-check your coordinate values from graphs, as small misreadings can affect the final answer.

Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.

Learn how to calculate the distance between two points using the distance formula. The example covers finding the distance between points (-4, 4) and (2, -2), rounding to the nearest tenth. Suitable for students in Grades 7-9.

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