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To find the distance between the points \((1, -1)\) and \((-4, 2)\), we use the distance formula:

\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the given points \((x_1, y_1) = (1, -1)\) and \((x_2, y_2) = (-4, 2)\):

\[
\text{Distance} = \sqrt{(-4 - 1)^2 + (2 - (-1))^2}
\]

Simplify the expressions inside the square root:

\[
\text{Distance} = \sqrt{(-5)^2 + (3)^2}
\]

\[
\text{Distance} = \sqrt{25 + 9} = \sqrt{34}
\]

Finally, calculate the square root and round to one decimal place:

\[
\text{Distance} \approx 5.8
\]

The distance between the points \((1, -1)\) and \((-4, 2)\) is approximately **5.8** units (rounded to one decimal place).

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. How is the distance formula derived from the Pythagorean theorem?
2. How would the distance formula change if we were working in three dimensions?
3. Can you find the midpoint of the line segment joining the points \((1, -1)\) and \((-4, 2)\)?
4. What is the distance between the points \((2, 3)\) and \((2, 7)\) in a 2D plane?
5. How does the distance formula relate to the concept of Euclidean distance?

**Tip:** Always double-check your arithmetic steps when using the distance formula to avoid small errors that can affect your final answer.

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

Learn how to find the distance between two points, (1, -1) and (-4, 2), using the distance formula derived from the Pythagorean theorem. A step-by-step solution is provided, making it easy for students in Grades 7-10 to understand.

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