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

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

Given the points $(1, 1)$ and $(-8, -3)$:

1. Assign the coordinates:

   • $x_1 = 1$, $y_1 = 1$
   • $x_2 = -8$, $y_2 = -3$

2. Substitute these values into the distance formula:

$d = \sqrt{(-8 - 1)^2 + (-3 - 1)^2}$

3. Simplify the expression:

$d = \sqrt{(-9)^2 + (-4)^2}$

$d = \sqrt{81 + 16}$

$d = \sqrt{97}$

So, the distance between the points $(1, 1)$ and $(-8, -3)$ is $\sqrt{97}$.

Would you like more details or have any questions? Here are some related questions:

1. How do you find the midpoint between two points?
2. What is the equation of the line passing through the points $(1, 1)$ and $(-8, -3)$?
3. How do you determine if two points are collinear with a third point?
4. What is the formula for the slope of a line?
5. How do you find the area of a triangle formed by three points?

Tip: When working with the distance formula, always ensure to subtract the coordinates in the same order (e.g., $x_2 - x_1$ and $y_2 - y_1$) to avoid mistakes.