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Midpoint Calculator + Online Solver With Free Steps
The Midpoint Calculator is an online tool that calculates the midpoint from numerous data points. When there are many numbers and you need to determine the midpoint, you’ll find the midpoint calculator to be helpful.
The Mid Point calculator uses two Cartesian coordinates to get the point that lies exactly between the two. This point is frequently used in geometry.
What Is a Midpoint
Calculator?
The Midpoint Calculator is an online tool that determines the middle point of a line segment. Both of the line segment’s endpoints should be equally distanced from it. In reality, it marks the halfway point for the line segment or the point at which a line segment is split into two equal parts. Every line segment has a distinctive midpoint.
A line segment AB, as we know, is a section of a line that is bounded by two different points A and B, which are known as the line segment AB‘s endpoints.
Point M, which splits the line segment AB into two congruent segments, AM $\approx$ MB, is the midpoint of the line segment.
Between a midpoint M and an endpoint, each segment has the same length. Section AB is frequently claimed to be divided in half by point M.
In other words, a line segment’s midpoint is its center or middle. The midway of every line segment is different.
Therefore, by applying the midpoint formula, we can determine the midpoint of any segment on the coordinate plane.
In 2-Dimensional Space (2D) midpoint (or mean) is also known as the median and simplifies calculations because there are just two endpoints.
This Midpoint Calculator can locate the endpoint of a line segment by using the start-point and midpoint coordinates since midpoints and endpoints are related words.
How To Use a Midpoint Calculator
You can use the Midpoint Calculator by following the instructions below.
Step 1
Fill in the provided input boxes with the given data points.
Step 2
Click on the “Submit“ button to determine the midpoint of the given data points and also the whole step-by-step solution for the midpoint calculation will be displayed.
How Does the Midpoint Calculator Work?
The Midpoint calculator works by using coordinates of two points A(xA, yA) and B(xB, yB) in the two-dimensional Cartesian coordinate plane and finding the halfway point between two given points A and B on a line segment.
It’s an online Geometry tool that requires 2 endpoints in the two-dimensional Cartesian coordinate plane.
It’s an alternate method to finding the midpoint of a line segment without a compass and ruler.
- Label the coordinates (x₁,y₁) and (x₂,y₂) and place the values into the formula.
- Add the obtained values in the parentheses and divide each value by 2.
- The new values will form the new coordinates of the midpoint.
- Check the results using the midpoint calculator.
If we have a line segment and want to cut that section into two equal parts, we will need to know the center. We can do this by finding the midpoint that we can measure with a ruler or a formula that involves the coordinates of each endpoint of the segment.
The midpoint is the specific average of each coordinate of the section, forming a new coordinate point.
Midpoint Formula
If we have the coordinates (x1, y1) and (x2, y2), the midpoint of these coordinates may be calculated using the formulas: \[ \frac{(x₁ + x₂)}{2}, \frac{(y₁ + y₂)}{2} \]
You may now refer to this as the new coordinate (x3, y3).
If the coordinates are entered, the midpoint calculator will instantly solve this. If you’re doing the math by hand, follow the procedures above.
It is straightforward to compute the midway by hand for small numbers, but the calculator is the fastest and most practical tool when dealing with bigger and decimal quantities.
By entering the coordinates of the endpoints into our Midpoint Calculator, you can quickly obtain the coordinates of the midpoint as well as the graph of the line segment and its endpoints.
The midpoint formula is frequently employed in ordinary problem-solving as well as in numerous scientific, technological, and economic disciplines.
Finding a “midpoint” is necessary, for instance, if you need to go from one place to another and wish to break it up into two days (i.e. a city roughly in the middle between the two cities).
Using the midpoint formula is the simplest method, albeit it’s not the best one if you don’t know the cities’ coordinates.
Real World Problems Using Midpoint
The midpoint calculator is mostly employed in analytical geometry because an ordered pair of numbers indicates the coordinates of a point in the two-dimensional Cartesian plane.
Additionally, it is utilized in other branches of mathematics, particularly in the study of complex numbers.
A complex number like z=a+ib is an example. The complex number is equivalent to the ordered set of numbers (a,b).
It implies that the midpoint of the segment connecting z1=a+ib and z2=c+id is the complex plane’s point $\frac{z_1+z_2}{2}$ with the coordinates: \[ (\frac{a+c}{2}, \frac{b+d}{2}) \]
The midpoint can also be used in physics. The center of mass of an item is sometimes referred to as its center of gravity. It’s the center of gravity, to put it another way.
The midpoint of a ruler, for example, serves as its balancing point. Any line segment’s point of equilibrium, the center of mass, or the center of gravity is at its midpoint.
Do We Round Midpoints?
Midpoints are generally not rounded. Since that point is an actual point in a data set, you do not round it off for continuous data.
In most cases, you don’t do it also for discrete data, instead noting that the midpoint is the average of the numbers on either side of the computation for the midway.
Solved Examples
Let’s explore some more examples regarding the Mid Point Calculator.
Example 1
Find the midpoint of the given line segment AB.
AB has endpoints at (7, 3) and (-5,5).
Solution
In this example, we want to find the midpoint of AB and it’s giving us the coordinates (x, y) of both endpoints.
So let’s start by plotting those endpoints A at (7, 3) and B at (-5,5) and then constructing the line segment will be AB.
So, we want to find the midpoint of this line segment manually without using the midpoint calculator.
Again we want to find the x,y coordinate, that is directly in the middle of this line segment. Such that it cuts it into two congruent halves pieces.
Here Coordinates of A are (7,3) and B (-5,5) so, now substitute the right values into the midpoint formula.
Now endpoints A and B are just XY coordinates.
Since (7,3) (-5,5) here in the first point 7 is x1 and 3 is y1 while in the second point -5 is x2 and 5 is y2.
\[ \text{Midpoint} =(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )\]
By putting values in the midpoint formula
\[ \text{Midpoint} =(\frac{(7+(-5))}{2}, \frac{(3+5)}{2}) \]
\[ =(\frac{2}{2}, \frac{8}{2}) \]
Mid Point =(1, 4)
So by using these endpoints in the midpoint formula we have found the coordinates of the midpoint of the AB at (1, 4).
So, the midpoint formula calculator works right in the same way as discussed above.
Example 2
Find the midpoint of a specific segment with endpoints (4,2) and (6,4).
Solution
As in the previous example. we have used the following formula to get the mid-point:
\[ \text{Midpoint} =(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )\]
In the above set of points, the values are:
X1 = 4, Y1 = 2, X2 = 6, Y2 = 4
Thus the mid-point would be given as:
\[ \text{ Mid Point} =(\frac{(4+6)}{2}, \frac{2+4}{2}) \]
\[ =(\frac{10}{2}, \frac{6}{2}) \]
Mid Point =(5, 3)
So, by using these endpoints in the midpoint formula we have found the coordinates of the midpoint of the line segment at (5, 3).
Example 3
Let’s assume that you know two points on a line segment and their coordinates are (6, 3) and (12, 7).
Find the midpoint using the midpoint formula.
Solution
\[ \text {Mid Point} =(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )\]
First, add the x coordinates and divide them by 2. This will give you the x-coordinate of the midpoint, XM.
\[ X_M =(\frac{x_1+x_2}{2})\]
\[ X_M =(\frac{6+12}{2})\]
\[ X_M =(\frac{18}{2})\]
XM= 9
Second, add the y coordinates and divide them by 2. This will ive you the y-coordinate of the midpoint, YM.
\[ Y_M =(\frac{Y_1+Y_2}{2})\]
\[ Y_M =(\frac{3+7}{2})\]
\[ Y_M =(\frac{10}{2})\]
YM = 5
Use each result to get the midpoint. In this example, the midpoint is (9, 5).