Saurav Sarkar

Pythagoras theorem- In a right angle triangle if we draw three squares on the three sides of the triangle then the area of the square drawn in the largest side of the right angle triangle (i.e. Hypotenuse) is equal to the sum of the area of the triangles drawn on the other two sides of the triangle. If the length of two right angle holding arms of a right angle triangle are 'a' and 'b'respectively and length of the hypotenuse is 'c' then - area of the triangle drawn on the hypotenuse = c*c sum of the area of the squares drawn on the other two sides of the triangle= a*a + b*b then by Pythagoras Theorem- a*a + b*b = c*c

Every two dimensional geometric figure is a path of a moving point. The path of the moving point maintaining fixed property or properties is called the locus of the moving point. E.g. suppose tip of your pen is a point. If you move your pen in your exercise copy maintaining a fixed rule then you will get a figure. Then tip of your pen will be considered as a moving point And the path is called the locus of the moving point. So from here you can conclude that any two dimensional geometric figure contains infinite number of points on it. Again any equation in two variables has infinite number of solutions and these solutions represents a two dimensional geometric figure. Now what will be the problem? The problem is how can we find that geometric figure which is represented by an equation of two variables? As I describe above- Every two dimensional figure has infinity number of points on it and every equation in two variable has infinity number of solutions so if we can construct an one- to - one corresponds between the points and the solutions of the equation then we can find the particular curve represented by that equation. Co- ordinate geometry is one kind of tool in mathematics that helps to form that one- to- one correspondence between the points and the solutions of the equation.