## Introduction of Midpoint Calculator

Before discussing about *midpoint calculator*, it is necessary to understand “What is midpoint?” Midpoint would be the location where you cut it in half to make two equal four-inched pieces e.g. Half of an eight inch pizza would be four inches so its midpoint will also be four. Calculation of midpoint is same like as we calculate the average of two numbers by adding together and dividing by two.

Now we extend this thinking to filling the midpoint of a line segment that connects two points by finding the point.

That point is directly in the middle of the line segment such that it cuts it into two congruent halves. In this case, you have line segment JK and point M is directly in the middle. So,**J M is ½** and **KM** is the other half. They are both congruent.

$$JM = KM$$

Midpoint calculator supports to calculate the middle of any two points A and B on a line segment. Actually midpoint calculator uses coordinates of two points as like $$A(xA,yA)A(xA,y A)$$ as well as $$B(xB,yB)B(xB,y B)$$x horizontally and y in parallel

Now let’s discuss about *midpoint calculator* briefly how its mechanism works.

## What is the Midpoint Formula

Now, we are going to be concerned with finding midpoints on the coordinate plane. So we want to think of a midpoint as a location with **XY (x,y)** coordinates and our tool here for finding the midpoint is going to be the *midpoint formula*

$$ (xm, ym) =({x^1+x^2\over 2},{y^1+y^2\over 2})$$

**(x _{m}, y_{m})** means coordinates of the midpoint

**(x _{1}, y_{1})** means coordinates of the first point

**(x _{2, }y_{2})** means coordinates of the second point

So let’s go ahead and learn how to use it.

## Example 1:

In this example we will know about that *how to find midpoint*.

AB has endpoints at (7, 3) and (-5,5). Plot point M the midpoint of AB.

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 line segment will be AB. So, we want to find the midpoint of this line segment. 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 end points A and B are just XY coordinates.

Since, (7,3) (-5,5) here in first point 7 is x1 and 3 is y1 while in second point -5 is x2 and 5 is y2.

$$=({x^1+x^2\over 2},{y^1+y^2\over 2})$$

By putting values in midpoint formula

$$=({7+(-5)\over 2},{3+5\over 2})$$

$$=({2\over 2},{8\over 2})$$

$$=(1,4)$$

So by using those 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 according the same way.

Example 2:

TN has a midpoint at (-3, -4) if T has coordinates (-6, -9), find the coordinates of N.

This example is more advanced than the first example. Here is a question not asking us *how to find midpoint *it’s giving us the midpoint of TN at -3, -4. It is also giving us the coordinates of one of the endpoints. This case T with coordinates -6, 9 and what we have to find is the coordinates of the other endpoint N so let’s visualize what’s going on here.

We know where the center of the line segment is and we know one of the end points. We want to find the other endpoint.

Here, T (-6, -9) N (? , ?)

As: (-6 is x1, -9 is y1) so by putting values in midpoint formula.

$$({x^1+x^2\over 2},{y^1+y^2\over 2})=\text{M is}\;(-3, -4)$$

We will start with the x coordinate of the midpoint at -3 so we know that (-6 +?) divided by 2 would have to equal -3.

$$=({-6+?\over 2},{y^1+y^2\over 2})$$

By solving this algebraically, it shows us that the unknown number will zero. Since -6 + 0 = -6 and – 6 divided by 2 would be equal to -3

$$=({-6+0\over 2},{y^1+y^2\over 2})$$

$$=(-3,{y^1+y^2\over 2})$$

So what we did was confirm the x coordinate in the midpoint. The -3 is both matchup and we know that the value of the x coordinate in endpoint N is zero.

N is (0,?)

Now we want to find out the value of y to an endpoint N. Now we know that the y value in the midpoint is -4. So we just want to find -9 + unknown value divided by 2 is going to equal -4. When we solve this algebraically, we should get 1 for that unknown value. Since -9 + 1 is equal to - 8 and -8 divided by 2 does equal to -4 which does match up with the y coordinate from the midpoint M and we can say that the value of y to an endpoint M is 1.

$$=({-3},{-9+?\over 2})$$

$$=({-3},{-9+1\over 2})$$

$$=({-3},{-8\over 2})$$

$$=(-3,-4)$$

Now you can plot the other end point with coordinate 0, 1 plotting this point allows us to construct the TN with midpoint M at -3 – 4.

Midpoint formula calculator also provides help to solve these types of advance problems. Note, Midpoint formula calculator and midpoint calculator are different names of the same mechanism.

To sum up this article I want to state one thing that the midpoint rule calculator practices the midpoint each interval as the point at which estimate the function for the Rieman sum. In actual Riemann sum, the values of the function and height of each rectangle is equal at the right endpoint while in a midpoint Riemann sum, rectangle height is equal to the value of the function at its midpoint.

I hope this article will be helpful regarding to understand the working of midpoint calculator.