Find the distance between the given points.  Round your answers to the nearest tenth if necessary.

(-1, 4) and (1, -1)

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

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

Substituting the coordinates \((-1, 4)\) and \((1, -1)\) into the formula:

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

Simplify the expression:

\[
d = \sqrt{{(1 + 1)}^2 + {(-1 - 4)}^2}
\]
\[
d = \sqrt{{2}^2 + {(-5)}^2}
\]
\[
d = \sqrt{4 + 25}
\]
\[
d = \sqrt{29}
\]

Now, take the square root of 29:

\[
d \approx 5.4
\]

So, the distance between the points \((-1, 4)\) and \((1, -1)\) is approximately **5.4** units.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How would you apply the distance formula in three-dimensional space?
2. Can you find the midpoint between these two points?
3. What is the equation of the line that passes through these two points?
4. How does the slope of the line compare to the distance between the points?
5. What is the distance between the points \((0, 0)\) and \((3, 4)\)?

**Tip:** If you don't have a calculator handy, you can approximate square roots by finding the two closest perfect squares and estimating between them.

Learn how to find the distance between two points (-1, 4) and (1, -1) using the distance formula. This problem covers key concepts in coordinate geometry and provides a step-by-step solution. Suitable for students in Grades 6-8.

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