Find the distance between each pair of points. Round to the nearest tenth.

(-4, 6) and (3, -7)

_ (decimal is .8)

To find the distance between two points \((-4, 6)\) and \((3, -7)\), we can use the distance formula:

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

Substituting the given points:

\[
d = \sqrt{(3 - (-4))^2 + (-7 - 6)^2}
\]

Simplifying:

\[
d = \sqrt{(3 + 4)^2 + (-7 - 6)^2}
\]
\[
d = \sqrt{(7)^2 + (-13)^2}
\]
\[
d = \sqrt{49 + 169}
\]
\[
d = \sqrt{218}
\]
\[
d \approx 14.8
\]

So, the distance between the points \((-4, 6)\) and \((3, -7)\) is approximately **14.8**.

Do you want more details, or have any questions? 

Here are 5 related questions to expand on this:
1. How does the distance formula relate to the Pythagorean theorem?
2. What is the distance between \((-2, 3)\) and \((5, -4)\)?
3. What happens if the two points lie on a straight line, either horizontally or vertically?
4. Can you find the midpoint of \((-4, 6)\) and \((3, -7)\)?
5. How would you calculate the distance if the points were in 3D space?

**Tip:** Always double-check your signs when applying the distance formula to avoid errors!

Find the distance between each pair of points. Round to the nearest tenth. (-4, 6) and (3, -7)

Learn how to calculate the distance between the points (-4, 6) and (3, -7) using the distance formula. This problem involves geometry and applying the Pythagorean theorem to find the distance on a coordinate plane. Suitable for students in Grades 7-10.

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