Find The Midpoint Of The Line Segment Shown Below
Midpoint =
The Correct Answer and Explanation is :
To find the midpoint of a line segment, we use the midpoint formula, which calculates the point exactly halfway between two given points. This point is equidistant from both endpoints and bisects the segment.
Midpoint Formula:
If the endpoints of the line segment are ( A(x_1, y_1) ) and ( B(x_2, y_2) ), the midpoint ( M ) is given by:
[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ]
Steps to Calculate the Midpoint:
- Identify the Coordinates: Determine the coordinates of the two endpoints.
- Add the x-Coordinates: Sum the x-coordinates of the two points.
- Divide by 2: Divide the sum of the x-coordinates by 2 to find the x-coordinate of the midpoint.
- Add the y-Coordinates: Sum the y-coordinates of the two points.
- Divide by 2: Divide the sum of the y-coordinates by 2 to find the y-coordinate of the midpoint.
- Combine the Results: The midpoint is the point with the x and y coordinates obtained in steps 3 and 5.
Example:
Consider two points ( A(2, 3) ) and ( B(4, 7) ).
- Add the x-Coordinates: ( 2 + 4 = 6 )
- Divide by 2: ( \frac{6}{2} = 3 )
- Add the y-Coordinates: ( 3 + 7 = 10 )
- Divide by 2: ( \frac{10}{2} = 5 )
Therefore, the midpoint ( M ) is ( (3, 5) ).
Applications of the Midpoint Formula:
- Geometry: Determining the center of a line segment, which is essential in constructions and proofs.
- Physics: Calculating the center of mass for two-point masses.
- Computer Graphics: Finding the center point between two pixels or objects.
- Navigation: Identifying the central point between two locations.
Understanding the midpoint formula is fundamental in various fields, as it provides a straightforward method to find the central point between two locations, aiding in analysis and design.
For a visual explanation, you might find this video helpful:
videoFinding the midpoint of a line segmentturn0search5