## Coordinate Geometry

### Cartesian plane

A  cartesian plane, named after the mathematician Rene Descartes, is a plane with a rectangular coordinate system that associates each point in the plane, with an ordered pair (x, y). The plane is called the cartesian plane, or the coordinate plane, or the xy-plane.

### Coordinate Axes

The coordinate plane has two mutually perpendicular axes which are number lines. The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where both the axes intersect is called the origin.

The horizontal line XOX′ is the x-axis and the vertical line YOY′ is the y-axis. The origin is at zero division on the x-axis and zero division on the y-axis.The positive numbers are labelled on the directions OX and OY. So, OX and OY are called the positive directions of the x - axis and the y - axis, respectively. Similarly, negative numbers are labelled on the directions OX' and OY'. So,OX′ and OY′ are called the negative directions of the x - axis and the y - axis, respectively.

The lines XOX'  and YOY' divide the plane into four equal parts. Each part is called a quadrant. The quadrants XOY, X'OY, X'OY', XOY' are called the first quadrant, second quadrant, third quadrant and fourth quadrant respectively.

### Coordinates of a Point

Distance of a point from y-axis is called the x-coordinate and the distance from x-axis is called the y-coordinate. (x, y) are called the coordinates of a point in the cartesian plane. If P(x, y) is any point in the cartesian plane, then 'x' is called the x-coordinate or the abscissa and 'y' is called the y-coordinate or the ordinate. Coordinates of origin are (0, 0).

The coordinates of a point on the x-axis are in the form of (x, 0) and that of a point on the y-axis are (0, y).
If (x, y) are the coordinates of a point, then (x, y) ≠ (y, x) and (x, y) = (y, x) if x = y.

### Equation of a Line

The equation of x- axis is y = 0 and equation of y-axis is x = 0. Equation of any line parallel to x-axis is y = k and equation of any line parallel to y-axis is x = k. The general form of equation of a line is ax + by + c = 0, where, a, b and c are real numbers and a ≠ 0 or b ≠ 0.