The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in the coordinate plane is given by the distance formula:

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

For the points $(4, 5)$ and $(-2, -3)$, we substitute these coordinates into the formula:

$d = \sqrt{(-2 - 4)^2 + (-3 - 5)^2}$ $d = \sqrt{(-6)^2 + (-8)^2}$ $d = \sqrt{36 + 64}$ $d = \sqrt{100}$ $d = 10$

Thus, the distance between the points $(4, 5)$ and $(-2, -3)$ is $10$.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How would the distance formula change in 3D space?
2. What is the midpoint of the segment connecting $(4, 5)$ and $(-2, -3)$?
3. Can you find the slope of the line passing through $(4, 5)$ and $(-2, -3)$?
4. What is the equation of the line through $(4, 5)$ and $(-2, -3)$?
5. How does the distance formula relate to the Pythagorean theorem?

Tip: Always check whether a given distance can be simplified into a radical form by factoring out perfect squares.