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The problem asks to calculate the distance between two points \( M(-1,4) \) and \( N(4,-1) \) in the coordinate plane, rounding to the nearest hundredth. We will use the distance formula for two points in a plane, which is:

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

Where:
- \( M(x_1, y_1) = (-1, 4) \)
- \( N(x_2, y_2) = (4, -1) \)

Let me calculate the distance.The distance between the points \( M(-1, 4) \) and \( N(4, -1) \) is approximately \( 7.07 \), rounded to the nearest hundredth.

Do you want more details or have any other questions?

Here are 5 related questions for practice:
1. How would the distance formula change if the points were three-dimensional?
2. What is the midpoint between the points \( M(-1, 4) \) and \( N(4, -1) \)?
3. How do you derive the distance formula from the Pythagorean theorem?
4. If you shift both points up by 3 units, what will the new distance be?
5. How can you calculate the length of a diagonal in a rectangle using the distance formula?

**Tip:** Always square the differences in the coordinates before summing them in the distance formula to avoid negative values.

Calculate the distance between the points M(-1, 4) and N(4, -1) in the coordinate plane. Round your answer to the nearest hundredth.

Learn how to calculate the distance between two points, M(-1, 4) and N(4, -1), using the distance formula. This problem involves geometry concepts and the Pythagorean theorem, perfect for students in Grades 8-10.

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