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To find the distance between the two points \((-1, -2)\) and \((4, 1)\), we can 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 \((-1, -2)\)
- \((x_2, y_2)\) is the second point \((4, 1)\)

Now, applying the values:

\[
d = \sqrt{(4 - (-1))^2 + (1 - (-2))^2}
\]
\[
d = \sqrt{(4 + 1)^2 + (1 + 2)^2}
\]
\[
d = \sqrt{5^2 + 3^2}
\]
\[
d = \sqrt{25 + 9} = \sqrt{34}
\]

Thus, the distance between the two points is \( \sqrt{34} \), which is approximately 5.83 units.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the midpoint of the two points \((-1, -2)\) and \((4, 1)\)?
2. How does the distance formula relate to the Pythagorean Theorem?
3. Can you calculate the slope of the line connecting these two points?
4. What is the equation of the line passing through these two points?
5. How would the distance change if one point was moved to \((4, 2)\)?

**Tip:** The distance formula is derived from the Pythagorean theorem and is used to measure the straight-line distance between two points on a plane.

Find the distance between the two pairs of points (-1, -2) and (4, 1).

Learn how to find the distance between two points (-1, -2) and (4, 1) using the distance formula. This step-by-step solution covers key concepts in coordinate geometry and the Pythagorean theorem. Suitable for students in Grades 7-9.

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