Math Problem Statement

Find the midpoint of the line segment whose endpoints are given (0.7, -2.9), (7.9, 2.4).

Solution

To find the midpoint of a line segment with endpoints (x1,y1,z1)(x_1, y_1, z_1) and (x2,y2,z2)(x_2, y_2, z_2), we use the midpoint formula for three-dimensional coordinates:

(x1+x22,y1+y22,z1+z22)\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right)

Given the endpoints (0.7,2.9)(0.7, -2.9) and (7.9,2.4)(7.9, 2.4), we assume these are in three-dimensional space, so the points are actually (0.7,2.9,0)(0.7, -2.9, 0) and (7.9,2.4,0)(7.9, 2.4, 0) by default. Using the formula:

Calculating Each Coordinate:

  1. X-coordinate: 0.7+7.92=8.62=4.3\frac{0.7 + 7.9}{2} = \frac{8.6}{2} = 4.3
  2. Y-coordinate: 2.9+2.42=0.52=0.25\frac{-2.9 + 2.4}{2} = \frac{-0.5}{2} = -0.25
  3. Z-coordinate: 0+02=0\frac{0 + 0}{2} = 0

Thus, the midpoint is: (4.3,0.25,0)(4.3, -0.25, 0)

Let me know if you'd like more explanation on this process or have any questions!

Additional Related Questions:

  1. How would you find the midpoint if given two points in a two-dimensional space?
  2. What is the formula for the distance between two points in three-dimensional space?
  3. How does the midpoint formula change if you only know two coordinates per point?
  4. Can the midpoint formula be extended to more than three dimensions?
  5. What are some real-world applications of finding a midpoint?

Tip: Always ensure you match the number of coordinates when using the midpoint formula, whether in 2D, 3D, or higher dimensions.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Midpoint Calculation

Formulas

Midpoint formula: ((x1 + x2) / 2, (y1 + y2) / 2)

Theorems

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Suitable Grade Level

Grades 8-10