When it comes to geometry, Midpoint and combinations are the two basic points to be kept in mind. Let’s discuss these things in detail:
What is a midpoint?
When a middle line is divided into two equal segments starting from the center it is known as the midpoint. Distance is equal to both the endpoints. The segment is bisected with this midpoint. In elementary school training, these both are considered instrumental concepts. It is usually applied in the cartesian system and is a very common term.
Notation
M is used for the midpoint
Formula:
(a+c)/2,(b+d)/2
It is one of the simplest formulae and has been in use for a long time.
How to find midpoint in geometry?
The midpoint of a Line Segment
- Add both “x” coordinates, divide them by 2.
- Add both “y” coordinates, divide by 2
- Is y= 2x – 4.9 a bisector of the line segment with endpoints at (–1.8, 3.9) and
(8.2, –1.1)?
I can solve this by using just a graph and the answer seems like yes. But one should always keep this fact in mind while solving a problem. The graph or picture only suggests the answer and makes its picture. Only algebra will tell you the exact answer. So e.g if I have been provided with a problem of a midpoint and need to find it, I will first apply the midpoint formula.
After solving it, I will tell you if this point is on the line or not?
y = 2x – 4.9
y = 2(3.2) – 4.9 = 6.4 – 4.9 = 1.5
In this case, I want y=1.4 but this is a bisector which is indicated by the graph picture. On the other hand, when I performed all the calculations it was proven by algebra that it’s not exactly a bisector. So, our answer will be no, it’s not a bisector.
Combinations in math
These are the ways to calculate the total outcomes of the event where outcomes order doesn’t matter. If order also matters its a permutation.
Formula for combination
nCr = n! / r! * (n – r)!
N is to show the total number of items
R represents the items chosen at a time.
Formula and concept
Coordinates of the midpoint are determined using it.
Example
Six friends want to play enough games of chess to be sure everyone plays everyone else. So, what are the total number of games they want to play?
Solution:
6 players can be taken in two at a time.
By using formula
This team will need a total of 15 players to play this game.
If you are not comfortable with doing all the calculations by hand you can use an online midpoint calculator and combination calculator.