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Point

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 Sub Topics The word Point is defined as the place, position or location in the space. There is no width, length and height of a point, it is also dimensionless. There is no dimension for the indication of point. Dimensionless means they do not have any volume, area, length. If we locate a point on a simple or standard plane then the point is known as origin. Suppose the tip of a pencil, corner of a Cube, or a dot on a sheet of paper. In two- dimension, the point is represented by an Ordered Pair. Suppose a point (a, b), where ‘a’ denotes the horizontal lines and ‘b’ represents the vertical lines. Many of the construction in the point Geometry consist of many more points. If we are going to define points, then any two points can be connected by a straight line. Point word was neither complete nor definitive. It only assumed facts about that what the point represents. The notation of points is generally defined in the geometry and topology. Suppose the teacher writing on the blackboard and fills the full board, then it also indicate the point. The fixed-point number is a number which presents the real thing i.e. data, collection of 5 books that means fix number of books, or we can say collection of fix number after a decimal point. Suppose we have value 2.123 then the point indicates that the 3 number after a decimal number and 1 number before a decimal number. It is also taken for the representation of the floating point number. We can represent fraction values with the help of points. Point increases the performance or accuracy of a number. The value which we are taken for data types is only an Integer value. If we are having 4 point on a plane surface, and if we join all these four points then we get a line, it means the Combination of points also give us a line. It is necessary to understand that a point is not a thing but it is a place. We represent the point by placing a dot with a pencil. Dot point has a Diameter, its diameter is around 0.22, but the point doesn’t have any size. Mainly upper-case letter were taken to represent a point. If there are many points and these entire point lie in a Straight Line, then they are known as collinear and these points lie on the same plane then it is known as coplanar.

Collinear Points

The basic elements of Geometry which form its foundation are points, lines and planes. A Point is a dot made on a plane by a sharp, pointed object, may be the tip of a pen or a pencil on a paper or even a hole made by piercing a pin in a paper. Points are represented by some capital letter. A point has neither length, nor breadth, nor thickness.

Two points joined together form a line. A line is straight & extends infinitely in both the directions. There is exactly one line passing through given two points. If there are more than two point the cannot be sometimes joined in a Straight Line. Only some points can be joined through the line while the others lay scattered and can be connected through different lines. This gives us the concept of Collinear Points in Geometry.

Collinear Points in geometry says that three or more points on a plane may or may not lie on the same line. If such three or more points lie on the same line, they are called Collinear Points. A point can not be collinear point and two points are always collinear. So to check collinearity of points there must be at least three points.

Theorem (If a Point Lies outside a Line, Then exactly One Plane contains the Line and the Point)

A theorem in Math can be regarded as a statement which is really true and a suitable proof of that fact can also be given.

Statement:
If a Point lies outside a line, then exactly one plane contains the line and the point.

Proof:
To prove our theorem, we will take help of some of the statements which are already assumed true although they do not have any proof. They are mentioned in the points given below:

1. If we have any two given points, then there can be just one line which passes through them.
2. If we are given any three points which are regarded as non collinear, then there can be one plane that passes through them.
3. If there is a line, then it will have two or more than two points.
4. If there is a plane, then it will have three or more than three non Collinear Points.
5. Whenever two planes intersect, they intersect by forming a line.
6. If there are two points in any plane, then this plane will also have the line joining these points.

So from the above given statements it is proved that if a point lies outside a line then exactly one plane contains the line and the point since a plane contains more than three collinear points and the line has two or more points(i.e, a plane has atleast a line and a point).