Math Problem Statement

Find the midpoint of the line segment joining points A and B. A(2, -5); B(4, 3).

Solution

To find the midpoint of a line segment joining two points, we use the midpoint formula:

M=(x1+x22,y1+y22)M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

Given:

  • Point A (2, -5)
  • Point B (4, 3)

Substitute the coordinates into the formula:

M=(2+42,5+32)M = \left( \frac{2 + 4}{2}, \frac{-5 + 3}{2} \right) M=(62,22)M = \left( \frac{6}{2}, \frac{-2}{2} \right) M=(3,1)M = (3, -1)

So, the midpoint of the line segment is (3, -1).

Would you like more details or have any questions?

Here are some related questions:

  1. How do you find the midpoint if the coordinates include fractions?
  2. What is the distance between points A and B?
  3. Can you explain how the midpoint formula is derived?
  4. How is the midpoint formula used in geometry beyond line segments?
  5. What is the relationship between the midpoint and the slope of the line segment?

Tip: The midpoint gives the exact center between two points, and it is often useful for dividing line segments equally or finding centers of geometric figures.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry
Midpoint of a Line Segment

Formulas

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

Theorems

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Suitable Grade Level

Grades 8-10