The image presents a problem where we need to find the distance between two points, K(-2, 10) and L(-4, 3), using the distance formula. The distance formula is:

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

Step-by-step solution:

1. Identify the coordinates of the points:

   • $K(x_1, y_1) = (-2, 10)$
   • $L(x_2, y_2) = (-4, 3)$

2. Plug the coordinates into the distance formula: $d = \sqrt{((-4) - (-2))^2 + (3 - 10)^2}$ Simplifying: $d = \sqrt{(-4 + 2)^2 + (3 - 10)^2} = \sqrt{(-2)^2 + (-7)^2}$

3. Calculate the squares: $d = \sqrt{4 + 49} = \sqrt{53}$

4. Therefore, the distance between the points K and L is: $d = \sqrt{53} \approx 7.28$

Would you like more details on any of these steps? Here are some related questions you might explore:

1. What are other methods to calculate distance between points in 3D space?
2. How does the distance formula relate to the Pythagorean theorem?
3. Can you find the midpoint between the points K(-2, 10) and L(-4, 3)?
4. How would you calculate the slope between points K and L?
5. How would this distance formula work for points on a different coordinate system, like polar coordinates?

Tip: When using the distance formula, always ensure that you square the differences between corresponding coordinates, so that negative differences don't affect the result!