https://file.aiquickdraw.com/mathbot/file/1727279584744s5e9x7d7.jpg

To solve this problem, we can use the distance formula:

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

where \((x_1, y_1)\) and \((x_2, y_2)\) are the two points.

For the points \((5, 9)\) and \((-7, -7)\), we can substitute into the formula:

- \(x_1 = 5\), \(y_1 = 9\)
- \(x_2 = -7\), \(y_2 = -7\)

Now, let's calculate the distance:

\[
d = \sqrt{{(-7 - 5)^2 + (-7 - 9)^2}} = \sqrt{{(-12)^2 + (-16)^2}} = \sqrt{{144 + 256}} = \sqrt{{400}} = 20
\]

So, the distance between the two points is 20 units.

Would you like a detailed breakdown or have any questions?

Here are 5 related questions for practice:
1. What is the distance between \((3, 4)\) and \((7, 1)\)?
2. If two points are \((2, 8)\) and \((10, -6)\), what is their distance?
3. How does the distance formula change in 3D space?
4. What is the midpoint between \((5, 9)\) and \((-7, -7)\)?
5. Can you calculate the distance between \((-3, 5)\) and \((6, 2)\)?

**Tip:** Always double-check the signs when substituting values into the distance formula!

What is the distance between (5, 9) and (-7, -7)?

Learn how to calculate the distance between the points (5, 9) and (-7, -7) using the distance formula. This problem involves coordinate geometry concepts and the Pythagorean theorem. Suitable for Grades 8-10.

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