Chapter: 4

What Are Coordinate Geometry ?

Cartesian System

• The system used for describing the position of a point in a plane is known as cartesian system.

• In this system, a plane is divided into four parts (called quadrants) with the help of two perpendicular lines.

Coordinate Axes And Origin

• The two perpendicular lines, which divides the plane, are called the coordinate axes.

• The horizontal line (XX’) is called the x-axis and the vertical line (YY’) is called the y-axis.

• The point of intersection of these lines is called origin and it is denoted by O.

Abscissa And Ordinate

• Abscissa of a point is its distance from the y-axis.

• Ordinate of a point is its distance from the x-axis.

Coordinates Of A Point

• If a is abscissa and b is ordinate of a point then (a, b) are called the coordinates of the point.

• In (a, b) a is also called the x – coordinate and b is also called the y – coordinate.

  • Here, the x – coordinate comes first and y – coordinate comes second. Therefore, (a, b) is an odered pair. If (a, b) ≠ (b, a) then, a ≠ b and if (a, b) = (b, a), then a = b.

• Coordinates of a point on the x – axis are of the form (a, 0) and that of the point on the y-axis are of the form (O, b).

• Coordinates of the origin are (0,0).

• Signs of the coordinates of a point in the first quadrant are (+ , +) in the second quadrant (–, +), in the third quadrant (–, –) and in the fourth quadrant (+, –).