Find the distance between the points.

(−1, 1), (3, −2)

To find the distance between the points \((-1, 1)\) and \((3, -2)\), we can use the distance formula:

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

Where:
- \((x_1, y_1)\) is \((-1, 1)\)
- \((x_2, y_2)\) is \((3, -2)\)

Now plug in the values:

\[
\text{Distance} = \sqrt{(3 - (-1))^2 + (-2 - 1)^2}
\]

\[
\text{Distance} = \sqrt{(3 + 1)^2 + (-2 - 1)^2}
\]

\[
\text{Distance} = \sqrt{4^2 + (-3)^2}
\]

\[
\text{Distance} = \sqrt{16 + 9}
\]

\[
\text{Distance} = \sqrt{25}
\]

\[
\text{Distance} = 5
\]

So, the distance between the points \((-1, 1)\) and \((3, -2)\) is \( \mathbf{5} \) units.

Would you like more details, or do you have any questions? Here are some related questions to explore:

1. Find the distance between the points \((2, 3)\) and \((5, 7)\).
2. What is the distance between the origin \((0, 0)\) and the point \((3, 4)\)?
3. Calculate the distance between the points \((6, -3)\) and \((-4, 2)\).
4. Determine the distance between the points \((7, 1)\) and \((7, -5)\).
5. How would the distance formula change if you were working in three dimensions?

**Tip:** Always double-check the signs of the coordinates when using the distance formula.

Discover how to calculate the distance between the points (-1, 1) and (3, -2) using the distance formula. This problem covers coordinate geometry and includes a step-by-step solution. Suitable for students in Grades 7-9.

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