Formula for Midpoint
In this session we will talk about the midpoint and what the Formula for Midpoint is. In mathematics most of the times we need to calculate the midpoint of a line or any object. A mid point is a point that is exactly between the two other points. For example we have a line that bisects or divides a given line segment into two equal parts or halves. The middle point or the intersection point of the lines is called the midpoint.
To get the midpoint of any two numbers we use a formula that is quite simple and make the calculations easy. For example if two numbers given are 5 and 15 then the exact half of the number is a number which lies within 5 and 15 and we can find it as (5 +15)/2 = 10. In this example we just added the given numbers and then the sum of the numbers is divided by 2.
The midpoint formula works in the similar manner, to find the exact half of two points then we just need to do the average of the x and y values.
The midpoint, M of the line segment from the given points p1 (x1, y1) to p2 (x2, y2) is given by ((x1 + x2)/2, (y1 + y2)/2).
Now we can understand the basic concept of this formula with the help of some formulas:
1. Find the midpoint between (1, 2) and (8, 9)
Then to solve this we have (x1 + x2)/2 and (y1 + y2)/2
(1 + 8)/2 and (2 + 9)/2
9/2 and 11/2
So the midpoint M (4.5, 5.2), this is the exact half of the given two points. Here we just did the average of the x and y values. This is very easy to solve.
2. Find midpoint of (2. 3, 4) and (8, 9)
Now the midpoint can be found by using the above mentioned formula.
(2.3 + 4)/2 and (8 + 9)/2
(6.3)/2 and (17)/2
So the midpoint is (3.15, 8.5).
- Is y = 2x – 5 a bisector of the line segment with the points (1, 8) and (8, 3)?
If we use graph for this question then the answer will be yes. But as we all know that a picture can only suggest us an idea of what is going on, but it cannot give an exact answer of the question. So for this we use algebra, now we can easily find the midpoint.
First we need to apply the midpoint formula:
M = (1 + 8)/2, (8 + 3)/2 = (4.5, 5.5)
Now we have to check if the point is on the line or not:
Y = 2x – 5
Y = 2(4.5) – 5 = 9 – 5 = 4
But here we need y = 5.5, so this shows that this line is close to become a bisector, but eventually it is not so the answer of this question is NO it’s not a bisector.
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