A midpoint is any point in the middle of a line that joins two points. The two reference points represent the endpoints of a line, with the midpoint lying in between two points. Furthermore, the midpoint divides the line that joins the two points for two halves. In case a line is drawn that divides the line that joins these two points. Thus, the line passes through the midpoint.
This article will show you exactly that by giving an in-depth explanation of the midpoint formula. As well as showing some great real-life applications of what you can use it for.
What is the Formula for Midpoint?
The Midpoint Formula finds the midpoint between two points whose coordinates are known to us. The midpoint formula is usable in finding the endpoint coordinates if we know the coordinates of the other midpoint.
A particular coordinate line is drawn to connect two points, (6, 3) and (4, 2). Then, the coordinates of the midpoint line joining these two points are (6+4)/2, (3+2)/2 = (10+5)/2 = (5, 2.5).
What is a Midpoint?
What is meant by midpoint? A midpoint refers to the point that lies between two points. Also, it remains in the middle of the line that joins two points. When a line is drawn joining the two points, the midpoint refers to a point at the center of the line for each of the two points. It remains equidistant from the two given points.
For example, the midpoint is B, given two points A and C. Point B remains located halfway between the two points, A and C. Therefore, calculating the midpoint, we can measure the segment's line and divide it by 2.
How to Find the Midpoint
The midpoint formula finds the exact center point between two defined points. This formula will take two number coordinates and find the exact center point by using the following method:
- Add both 'x' coordinates, divide by 2 (this will be your new x coordinate)
- Add both 'y' coordinates, divide by 2 (this will be your new y coordinate)
This formula is used in many different applications, from math to science. A graphing calculator can also be used to find the midpoint.
Real-Life Example of Midpoint Formula
The midpoint formula is the simplest and will work on any line segment. It is defined as:
M = [(x 1 + x 2 )/2 , (y 1 + y 2 )/2]
where M is the midpoint, (x 1, y 1 ) and (x 2, y 2 ) are the coordinates of each endpoint on a line segment.
Example: Find the midpoint of the line segment with endpoints (3, 4) and (-3, 5).
Solution:
M = [(x 1 + x 2 )/2 , (y 1 + y 2 )/2]
M = [(3+-3)/2 , (4+5)/2]
M = [0 , 9/2]
The midpoint is [0, 4.5].
What Is the Midpoint Formula in Coordinate Geometry?
One common application for the formula is in the field of geometry. Therefore, what is the midpoint formula in geometry? Deriving the midpoint formula geometry is a simple exercise in coordinate geometry. The point of intersection of two perpendicular lines divides each of them in half, and the geometric center of a quadrilateral divides the distance for two opposite vertices into two halves.
The midpoint is the average (arithmetic mean) of x-coordinates and y-coordinates. For example, consider the points (2, 3) and (4, 5). The average of 2 and 4 is 3, and the average of 3 and 5 is 4. Therefore, the midpoint lies at (3, 4).
If you have only one pair of coordinates, your midpoint is simply that pair of coordinates. If you have more than two pairs of coordinates, then your midpoint is their average — that is, add them up and divide by the number of pairs.
How to Use Coordinates to Determine the Distance Between Two Points
To calculate the midpoint between two points, you need to add both x-coordinates together, divide by two, and then add both y-coordinates together and divide by two. The resulting coordinate is the location of the midpoint. The formula would look like this:
Midpoint = (x1 + x2) / 2, (y1 + y2) / 2
Here's an example of how you would use this equation to find midpoint between two points: (2, 3) and (6, 8).
Midpoint = (2 + 6) / 2, (3 + 8) / 2
Midpoint = 4, 5.5
The answer is (4, 5.5). You can verify this with a calculator or a graphic calculator.
Final Takeaway
The midpoint formula is pretty easy to remember, especially if you use a mnemonic device like the one above. The biggest takeaway should be how simple the midpoint formula is. There are no square roots or crazy-complicated operations—just three steps.
Memory tricks and other mnemonic devices can help remember the midpoint formula, especially if you find math intimidating or need a little help in that department. But even without tricks, it 'sits still pretty straightforward.
Are you struggling with finding the distance with two points using the midpoint formula? Reach out to Acemyhomework for professional assistance from experts today.
