It is for sure, you will love to solve the problems that are based on the formula of Midpoint. With  regular practice, you will develop the competence to correctly solve the toughest problems in this category, and this will enable you to scope better  marks in Mathematic as well. Once, you are provided with the information for the endpoints of a line, you can easily find out its midpoint, applying this formula. Working on these problems, you will get to know the tricks to compute  the value of the Coordinates of the endpoints for a given line, in case, you are served with the information for one of the endpoints as well as the midpoint of the line segment. 

What is the formula to find the midpoint of a line segment?

The computation of the midpoint of a line segment involves the average values of the X and Y Coordinates. The purpose of applying the Midpoint Formula is to explore the coordinates, for the midpoint of a given line segment, along the X-Y plane. The basic formula to find the midpoint of a line runs as follows:

(X,Y) = (X+X1/2, Y + Y1/2)

Alternatively, the purpose of this formula is  to evaluate the average values for the X and Y coordinates. 

The logic beyond the formula can be explained with the following example:

Let’s assume the points A with Coordinate 1 & 5, and B with coordinates 7 &3, and you need to find the midpoint for the line AB. 

Now, to solve this problem, you will need to substitute the given values to the basic formula stated above. This will run as X,Y = 1+7/2, 5+3/2. Now, if the like values are combined, it will come like, X,Y = 8/2, 8/2. Upon division, the equation will shape like X,Y = 4,4 which is the respective value for the X and Y Coordinates. 

Is it possible to find the midpoint, wherein the value for only one end point along wit the slope value is served?

It  is possible to find the Midpoint of a given line segment, if you are served with the value for one of its endpoints. In a similar instance, you need to be provided with the information for the slope of the line as well. you simply need to use the Midpoint Formula

For instance, Assume, M is the slope for the line AB with the Coordinates of the end point B is (4,-3), and now, you need to find the coordinate for the point A. 

In this case as well, you need to substitute the given values into the equation. This will read the equation like:

X,Y = 4+X/2, -3+Y/2

Now, you need to separate the equation to find the values for X and Y individually;

-3 = 4+X/2 

-6= 4 +X

X= -10

Similarly, you need to find the value for Y;

-1 = -3 +Y/2

-2 = -3 +Y

Y= 1 

Thus, you will get the values for X, Y as -10,1. 

Overview of the formula to calculate Midpoint 

Complying with the X,Y system, assume two points, A and B. The midpoint of the line AB should lie somewhere in the middle of these 2 end points. As both these end points will value X, Y for their coordinates, the same will be the case for the midpoint of this line. Now, let’s consider the value of the Coordinates  of the point A as X1, Y1, and for that of the point B, let’s assume the Value to be X2, Y2. 

As for the midpoint of this line segment, not only it will lie midway between these end points, but, between the X and Y Coordinates as well.  Now, one can assume the Coordinates of the Midpoint to be Xm and Ym and the value of the coordinate of the Midpoint is going to be the average of the 2 coordinates. In that case, the formula should run as :

(X1+X2)/2, (Y1+Y2)/2 

Now, you need to substitute the given values for the coordinates that will find the exact coordinate for the midpoint of the line segment AB. Thus, finding the midpoint for any given line is not going to be a big deal, applying this formula. 

What to do, if you are unable to master the problems based on this formula?

It is obvious that, while you will start learning this formula for the first time, you will face some issues in remembering it and correctly applying the formula. Don’t worry, as every new learner takes his/her own time in learning new things, and as such, you  must allow yourself that time to acquire the right skill and expertise in solving these problems. Here some of the tricks and tips that will enable you to rightly recall the formula and correctly solve the problems, based on this formula:

  • No matter what you are doing and wherever you are, you can go about just try the memory technique to recall the formula. This is a simple and effective technique to remember and recall any Mathematical formula, without the need to put excessive efforts. So, it will be really worthy to try this trick. 
  • There can be no alternatives that regularly and rigorously solving the problems based on this formula. This will enable you to understand the formula better, and with regular practice, you will get into a position, wherein you can solve the similar problems correctly, with confidence. 
  • It will never help you, if you start to panic with the problems that are to be solved using this formula. Rather, you should face such problems with confidence that will enable you to solve the problems easily. 
  • In case, you are facing issues in understanding the formula, don’t hesitate to seek second or subsequent advices from your teacher. It is always better to do so, rather than pretending that you have understood the formula, while, you are still having doubts and confusions about it, in the back of your mind. 

These simple tricks and tips will enable you to master the Midpoit Formula within the minimum time.