The formula which is applied in order to find the middlemost of the centermost point on a given straight line that is infinite is defined as the midpoint formula. Have you heard about the term, median? It is also considered as the middlemost point of a given observation. For example, in a given observation of 3, 4, 6, 8, 10. The number 6 is considered as the median or middle number of the given data.

Similarly, this formula is applied to get a coordinate or coordinates of the line which is straight in nature. Let us assume that in a given straight line, there are three points namely: A, B, and C. The points ‘A’ and ‘C’ are the initial and terminal points, therefore the middle point or midpoint is B. When the values are given algebraically, we use a formula that shall be covered in a detailed manner in the next few sections. 

Some Significant Points To be Remembered for Midpoint Formula

As mentioned above, a midpoint is a point in a straight line that is situated between two different points which are also known as the initial and terminal points. There are some important notes to be remembered while you calculate a question about the midpoint formula. The following points mentioned below analyses those points.

  • Whenever you calculate a problem about this topic, always remember that the midpoint in a straight line will divide the segment of the line in the ratio of 1:1. 
  • A midpoint will always divide the straight line or the segment of a line into exactly two equal parts. You may observe that the bisector will always cut at the midpoint of the line segment. 
  • A midpoint of any line which is not curved can be calculated in two ways: if the line is horizontal or vertical, you may divide the measurement of the line by 2 to get the midpoint, the second way of calculating or finding the middlemost point is by the midpoint formula. 

Some Calculations based on the Midpoint formula

Example 1: Let’s suppose there is a straight-line AB with coordinates (2,4) and (4,6). How do you find the midpoint of the straight line using the midpoint theorem? 

Let the coordinates be (x,y) and (a, b). The midpoint formula is {(x+a)/2, (y+b)/2}

On substituting the values in the formula, we get the midpoint of the straight line as {(2+4)/2, (4+6)/2} which on simplified is equal to {(6)/2, (10)/2} = (3,5)

Example 2:  Let’s suppose there is a straight-line AB with coordinates (-2,4) and (4,6). How do you find the midpoint of the straight line using the midpoint theorem? 

Let the coordinates be (x,y) and (a, b). The midpoint formula is {(x+a)/2, (y+b)/2}

On substituting the values in the formula, we get the midpoint of the straight line as {(2+4)/2, (4+6)/2} which on simplified is equal to {(2)/2, (10)/2} = (1,5)

So, the midpoint of line AB is equal to (1,5).

If you want to know more about midpoint formulas, you can visit the Cuemath website to understand the topic in a fun and interesting way.

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