Geometry is the branch of mathematics that which deals with shapes of objects and its relative position in space.
When considering position, if we are only dealing with the two dimensions, then it is called plane geometry or simply two dimensional geometry.
Similarly, if we are dealing with all the three dimensions, then it is called solid geometry or simply three dimensional geometry.
Plane geometry ( two dimensional geometry).
As explained if we are only dealing with the two dimensions, it is called plane geometry or two dimensional geometry. By Plane geometry we can represent any figures that can be drawn on a plane surface or paper like points, lines, triangles, rectangles, circles, polygons etc. But we cannot represent three dimensional objects or solids by using two dimensional geometry
Three dimensional geometry
In solid geometry or simply three dimensional geometry we deal with all the three dimensions. By using three dimensional geometry we can represent any figures that can be represented in two dimensional geometry and in addition to that all three dimensional figures or solids that which cannot be represented in two dimensional geometry.
Coordinate system can be explained as the method or process of representing the position of an object in space. Commonly used coordinate systems are Cartesian coordinate system and Polar coordinate system.
Cartesian coordinate system
In Cartesian coordinate system or rectangular coordinate system or simply planar coordinate system an object is represented by its perpendicular distance from the axes.
Axes, origin and Coordinates of an object
The three axes are generally notated as $x$, $y$ and $z$. These axes are perpendicular to each other. Each axis can be taken as a straight line moving in both directions or as a number line. The point at which the three axes intersect to each other perpendicularly is called origin. At origin the value of $x$, $y$ and $z$ axes are always zero. Coordinate of an object in space is the perpendicular distance of that object to each axis and is denoted as ($x$, $y$, $z$)
Polar coordinate system
Polar coordinate system can be simply explained as the system of representing the position of an object in by means of its direct distance from origin and the angle it makes.