To solve for the distance between the two points $(-2,1)$ and $(-7,5)$, we use the distance formula:

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

Where:

• $(x_1, y_1)$ is the first point $(-2, 1)$
• $(x_2, y_2)$ is the second point $(-7, 5)$

Now, substituting the values:

$d = \sqrt{(-7 - (-2))^2 + (5 - 1)^2}$ $d = \sqrt{(-7 + 2)^2 + (5 - 1)^2}$ $d = \sqrt{(-5)^2 + (4)^2}$ $d = \sqrt{25 + 16}$ $d = \sqrt{41}$

Thus, the distance between the two points is:

$d \approx 6.4$

Would you like more details on any part of this calculation?

Here are 5 related questions you might find useful:

1. How do you calculate the midpoint between two points?
2. What is the formula for finding the slope between two points?
3. How do you apply the Pythagorean theorem in the distance formula?
4. Can the distance between points ever be negative?
5. How is the distance formula derived from the Pythagorean theorem?

Tip: Remember that the distance between two points in a plane is always a positive number!