The basic study of Analytical Geometry involves the study of different points on the plane, which are marked at the (x, y) coordinates. If we study about the Analytical Geometry, it will include the study of the points on the Cartesian plane of the different geometrical figures and then further analyzing the properties of these figures and the graphs, based on the observations and their properties too. It also includes the study of the
coordinate geometry. The study of Analytical Geometry basically involves the study of algebra on the graph. If we need to plot any line or the pair of lines, we come to the conclusion that the lines are having which of the following properties:
Are the two lines plotted on the graph are parallel.
Do the two line plotted on the graph have any point of intersection.
Or are the two lines plotted on the graph, which are represented by different lines, are representing the same pair of lines and they coincide with each other at all the points. It indicates that the two lines are over lapping.
When we talk about the
coordinate geometry, we mean that any point of the line is to be represented on the Cartesian plane and they are represented in form of the ordered pairs. We say an ordered pair of number a and b listed in a specific order, with a at a first place and b at the second place is called an ordered pair of the plane (a, b).
We represent all the points on this plane in the form of an ordered form of the real numbers, to which we call the coordinates of the particular point in the plane. This branch of mathematics in which we solve all the geometrical problems by the help of the coordinate system of solving the algebraic equations is called Analytical Geometry. There exist two coordinates of the plane, namely x – axis and the y- axis. The two axes are perpendicular to each other and the meeting point of the two axes is called the origin. The coordinates of the origin are (0, 0). The horizontal line is called X O X’ and the vertical line is called Y O Y’. We call these lines as the coordinate axis or the axis of reference. The horizontal line is called the x – axis and the vertical line is called the y – axis.
The distances measured from OX and OY are all positive numbers and on another hand the distances measured on the OX’ and OY’ are all negative values.
The plotting of the graph is done on the basis of the points which are located on the graph to represent any particular line or curve.
The two coordinate axis divide the plane into four regions, which are called as quadrants. These quadrants are named as I, II, III and IV quadrants. Following are the signs of the coordinates
I - ( +, + )
II – ( -, +)
III – ( -, - )
IV – ( +, -)