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).
Two dimensional PlaneBack to Top
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 PlaneBack to Top
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.