what is the midpoint of the segment shown below

Guri Bee

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20-10-2024

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Finding the Midpoint: A Simple Guide

Understanding the midpoint of a line segment is crucial in geometry and various applications. Let's explore how to find the midpoint using the provided diagram and delve into the concept.

The Diagram:

Unfortunately, you haven't provided a diagram! To illustrate this concept, let's assume we have a line segment with endpoints A(2, 4) and B(8, 10).

What is the Midpoint?

The midpoint of a line segment is the point that divides the segment into two equal parts. It's essentially the "middle" point of the segment.

How to Find the Midpoint:

The midpoint formula is straightforward and can be used for any line segment. It's derived from the average of the x-coordinates and the average of the y-coordinates of the endpoints.

Formula:

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

where:

• (x1, y1) are the coordinates of the first endpoint
• (x2, y2) are the coordinates of the second endpoint

Applying the Formula to Our Example:

1. Identify the endpoints:

   • A(2, 4) => (x1, y1)
   • B(8, 10) => (x2, y2)

2. Plug the values into the formula:

   • Midpoint (M) = ((2 + 8)/2, (4 + 10)/2)

3. Simplify:

   • Midpoint (M) = (10/2, 14/2) = (5, 7)

Therefore, the midpoint of the line segment with endpoints A(2, 4) and B(8, 10) is (5, 7).

Practical Applications:

Understanding the midpoint has various practical applications in fields like:

• Geometry: Calculating the center of a shape or finding the location of a specific point in a figure.
• Computer Graphics: Defining the center of an object in 2D or 3D space for rotation, scaling, or other transformations.
• Civil Engineering: Locating the center of a bridge or determining the midpoint of a road segment for planning purposes.

Conclusion:

The midpoint formula is a valuable tool for finding the middle point of any line segment. Its simplicity and versatility make it useful in various mathematical, geometrical, and engineering applications.