The image asks to "Find the distance between (5, 8) and (7, -4)."

To calculate the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane, we use the distance formula:

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

In this case:

• $(x_1, y_1) = (5, 8)$
• $(x_2, y_2) = (7, -4)$

Substituting into the formula:

$d = \sqrt{(7 - 5)^2 + (-4 - 8)^2}$ $d = \sqrt{(2)^2 + (-12)^2}$ $d = \sqrt{4 + 144}$ $d = \sqrt{148}$ $d \approx 12.17$

Thus, the distance between the points $(5, 8)$ and $(7, -4)$ is approximately 12.17 units.

Would you like a detailed breakdown of any step, or have other questions?

Here are 5 related questions:

1. What is the formula to find the midpoint between two points?
2. How do you apply the Pythagorean theorem to find the distance between points?
3. Can the distance formula be used in three dimensions? If so, how?
4. What is the geometric interpretation of the distance formula?
5. How would you find the slope between the points $(5, 8)$ and $(7, -4)$?

Tip: When calculating distances, always ensure to square the differences before adding to avoid errors with negative signs.