Co-ordinate Geometry(Triangles-Straight lines)

May 28, 2014

Co-ordinate Geometry

(Triangles-Straight lines)

Co-ordinate Geometry is also called Analytical Geometry. It is the branch of Geometry in which we use two numbers, called Co-ordinates to indicate the position of a point in a plane.

Any point in a plane can be located in position with reference to two mutually perpendicular lines called "Co-ordinate Axes" or simple "axes". The horizontal reference line is called the x-axis, and the vertical reference line is called the y-axis.

As Shown in the below figure , XX' is the x-axis and YY' is the y-axis. The point of intersection of these two axes is called origin.

Let P be any point in the plane. From P draw PM perpendicular to OX. Then the lengths of OM and MP are called the co-ordinates of P(usually denoted by x and y respectively). The length of OM is called the x co-ordinate or the abcissa and the length PM is called the y co-ordinate or ordinate of P. Hence a point P can be denoted as P(x,y).

The axes divide the plane into 4 equations as shown below.

Sign convention:

Distances measured along OX and OY are positive whereas the ones measured along OX' and OY' are negative. The signs of the co-ordinates x and y depends on the quadrant in which the point lies.

I Quadrant x-co-ordinate is positive

y-co-ordinate is positive

II Quadrant x-co-ordinate is negative

y-co-ordinate is positive

III Quadrant x-co-ordinate is negative

y-co-ordinate is negative

IV Quadrant x-co-ordinate is positive

y-co-ordinate is negative

Note 1: The co-ordinate of origin are (0,0)

Note 2: The ordinate of every point on x-axis is Zero.

Note 3: The abscissa of every point on y-axis is zero.

Some basic rules and formulas are given below, which have to be remembered. Each formula is followed by one or more examples, which clearly explain its application.