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Origin of Plane


The Point where the horizontal axis and vertical axis meet is called origin of plane. We can easily understand this with the help of Coordinate Plane. A coordinate plane consists of two axes (plural of axis) and four quadrants because of this structure of coordinate plane is rectangular. Left side of horizontal axis contains negative number and right side has positive Numbers. Upper part of vertical number line or axis has positive numbers and lower part has negative numbers. The point where both axes meet is known as origin. The coordinates of origin or point of Intersection of x- axis and y- axis is given by (0, 0).
While plotting the points on the plane we start the counts from the origin so that we can place them on the accurate Position. The x-axis is known as Abscissa and the y-axis is known as Ordinate.
The origins are present in both two-dimensional and three-dimensional planes. In two-dimensional plane four quadrants are present and in three-dimensional plane the plane is divided into eight parts which are known as octants. In two-dimensional planes at the top and extreme right side is 1st quadrant then the rest are in anti clockwise manner, at top left second quadrant is present, at bottom left below second quadrant is third quadrant and at bottom right below first quadrant is fourth quadrant.
Although there is no specified nomenclature but we generally write it in the roman number form it is considered as the best way of representation. The coordinate system is also known as Cartesian coordinate system. This is all about origin of plane.

Two dimensional Plane

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In our day to day life we see different shapes, some shapes are two dimensional and some are three dimensional shapes. Here we will discuss different types of shapes which are related to two- dimensional plane.
Two dimensional plane includes shapes which have two dimensions and these shapes are shown below:
Triangle, quadrilateral, square, pentagon, hexagon, heptagon, octagon, hendecagon, and dodecagon etc.
These shapes have two dimensions therefore they are included in two dimensional plane.
Now we will discuss about these shapes:
Triangle: As we know that three sides are present in a triangle. It is also known as Trigon, the sum of interior angle of a triangle is 1800 and one interior angle is of 600.
The formula for finding the perimeter and area of a triangle is given by:
Perimeter = a + b + c;
Area = base * altitude / 2;
Quadrilateral: Four sides are present in a quadrilateral; interior angle of quadrilateral is of 900.
Square: As we know that Square have four sides, all the sides of a square are of equal length. All the internal angle of a square is 90 degree.
The formula for finding the perimeter of a square is given by:
Perimeter = 4s;
The area of a square is given by:
Area = s2, where‘s’ denotes the sides of a square.
Pentagon: Five sides are present in a pentagon and the interior angle of a pentagon is 108 degree.
Hexagon: Six sides are present in a Hexagon and the interior angle of hexagon is 120 degree.
Heptagon: In a heptagon seven sides are present and the interior angle is approximately 128.5710.
Octagon: Eight sides are present in an octagon and the interior angle of octagon is 1350.
Hendecagon: Eleven sides are present in a hendecagon and the interior angle of a hendecagon is 147.2730.
This is all about two dimensional plane.

Three dimensional Plane

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Three dimensional plane can be defined as a plane which contains three axis i.e. x, y and z- axes. We can plot different three dimensional objects like Tetrahedron, cube, octahedron, dodecahedron, icosahedron on a 3- dimensional plane. We can also plot hypersphere in three dimensional space. Let's have small introduction about hypersphere. Hypersphere can be defined as a Set of points in three dimensional plane situated at fixed distance 'r' from central Point 'A'. So the volume of a hypersphere is given as: volume = 4 / 3 * pi * r3. Here 'r' is the radius of hypersphere. Now we will talk about some properties of three dimensional space. Properties of three dimensional plane do not hold for higher dimensions.
In three dimensional plane either two planes are parallel or they bisect a line.
In plane a line is either parallel, bisects at only single point, or contained in plane. These all are properties of three dimensional plane.
Now we will see methods for defining a plane.
Suppose we have A1 = (x1, y1, z1), and A2 = (x2, y2, z2), A3 = (x3, y3, z3) are non – collinear points.
So plane passes through points A1, A2, A3 and defined as a set of points (x, y, z) which satisfy the given determinant equations:| x – x1 y – y1 z – z1 | | x – x1 y – y1 z – z1 |
| x2 – x1 y2 – y1 z2 – z1 | = | x – x2 y – y2 z – z2 | = 0
| x3 – x1 y3 – y1 z3 – z1 | | x – x3 y – y3 z – z3 |
This is all about three dimensional space.