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Part 1
Find the distance between the pair of points.
Upper N left parenthesis negative 4 comma negative 14 right parenthesis​, Upper P left parenthesis negative 4 comma negative 5 right parenthesis

To find the distance between the two points \( N(-4, -14) \) and \( P(-4, -5) \), we can use the distance formula:

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

Given the points \( N(-4, -14) \) and \( P(-4, -5) \), the coordinates are:
- \( x_1 = -4 \), \( y_1 = -14 \)
- \( x_2 = -4 \), \( y_2 = -5 \)

Substituting these values into the distance formula:

\[
d = \sqrt{(-4 - (-4))^2 + (-5 - (-14))^2}
\]

Simplifying the expression:

\[
d = \sqrt{(0)^2 + (-5 + 14)^2}
\]
\[
d = \sqrt{0 + 9^2}
\]
\[
d = \sqrt{81}
\]
\[
d = 9
\]

So, the distance between the points \( N(-4, -14) \) and \( P(-4, -5) \) is **9 units**.

Would you like further details or have any questions?

Here are some related questions you might find helpful:
1. What is the distance formula in 3D space?
2. How do you find the midpoint between two points?
3. Can the distance formula be applied to real-world problems?
4. What are the properties of vertical and horizontal distances in a coordinate plane?
5. How can you find the distance between two points using Pythagorean theorem?

**Tip:** The distance between two points with the same x-coordinates (or y-coordinates) simplifies to the absolute difference between the y-coordinates (or x-coordinates).

Learn how to calculate the distance between two points (-4, -14) and (-4, -5) using the distance formula. This problem involves basic coordinate geometry and the application of the distance formula. Suitable for students in Grades 6-8.

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