To find the distance between the points $(7, -7)$ and $(9, -9)$ and form a right triangle, we can follow these steps:

1. Calculate the horizontal and vertical distances:

• Horizontal distance: The difference in the $x$-coordinates is $9 - 7 = 2$.
• Vertical distance: The difference in the $y$-coordinates is $-9 - (-7) = -2$, which has an absolute value of 2.

2. Use the Pythagorean theorem:

Since the two distances form the legs of a right triangle, with the segment between $(7, -7)$ and $(9, -9)$ as the hypotenuse, we can apply the Pythagorean theorem: $\text{Distance} = \sqrt{(2)^2 + (2)^2} = \sqrt{4 + 4} = \sqrt{8} \approx 2.8$

Final Answer:

The distance between the points, to the nearest tenth, is approximately 2.8 units.

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

Here are some related questions:

1. How do we apply the Pythagorean theorem in coordinate geometry?
2. What is the general distance formula for two points?
3. How can we determine if a triangle is a right triangle based on coordinates?
4. Why is it important to understand distance in coordinate systems?
5. How do different quadrants affect distance calculations?

Tip: When working with coordinates, always double-check the signs of differences to avoid calculation errors.