Let's calculate the distance between each pair of points in the given graphs using the distance formula:

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

I will analyze the points from each graph:

For Graph 1:

• Points: (-2, 3) and (3, -1)

$d = \sqrt{(3 - (-2))^2 + (-1 - 3)^2}$

$d = \sqrt{(3 + 2)^2 + (-1 - 3)^2}$

$d = \sqrt{5^2 + (-4)^2}$

$d = \sqrt{25 + 16} = \sqrt{41} \approx 6.4$

For Graph 2:

• Points: (-4, -2) and (2, 2)

$d = \sqrt{(2 - (-4))^2 + (2 - (-2))^2}$

$d = \sqrt{(2 + 4)^2 + (2 + 2)^2}$

$d = \sqrt{6^2 + 4^2}$

$d = \sqrt{36 + 16} = \sqrt{52} \approx 7.2$

Final Answers:

1. Graph 1: Distance = 6.4 (rounded to the nearest tenth)
2. Graph 2: Distance = 7.2 (rounded to the nearest tenth)

Would you like me to explain any steps in detail or calculate something else? Here are some follow-up questions:

1. Can you identify where the distance formula is derived from?
2. Would you like a graph or visualization of these calculations?
3. Should I explain how to approximate square roots?
4. Do you need help generalizing this formula for 3D space?
5. Would you like to verify these calculations with another method?

Tip: When finding distances, always carefully substitute the coordinates to avoid sign errors.