Math Problem Statement

Question content area top 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

Solution

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

d=(x2x1)2+(y2y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Given the points N(4,14)N(-4, -14) and P(4,5)P(-4, -5), the coordinates are:

  • x1=4x_1 = -4, y1=14y_1 = -14
  • x2=4x_2 = -4, y2=5y_2 = -5

Substituting these values into the distance formula:

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

Simplifying the expression:

d=(0)2+(5+14)2d = \sqrt{(0)^2 + (-5 + 14)^2} d=0+92d = \sqrt{0 + 9^2} d=81d = \sqrt{81} d=9d = 9

So, the distance between the points N(4,14)N(-4, -14) and P(4,5)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).

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Distance Formula

Formulas

Distance formula

Theorems

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Suitable Grade Level

Grades 6-8