Learning objective

- Understand Cartesian coordinate system
- Identify coordinate axes and coordinate of points
- Find the distance between two points
- Find the coordinates of midpoint
- Find the Gradient / Slope
- Find the equation of line joining two points

**Cartesian plane**

The Rectangular coordinate system consists of two perpendicular number lines, called coordinate axes.

The horizontal line is x axis and the vertical line is y axis, the meeting point of the horizontal and vertical lines called origin ‘O’. This XOY plane is called the cartesian plane.

The position of any point P on the cartesian plane can be expressed as a combination of its horizontal ( x-axis) and vertical (y – axis ) distance from the origin.

The x-coordinate is called the abscissa and the y-coordinate is called the ordinate of the point

**I. Points on Co ordinate (Cartesian) plane**

**2. Distance between two points**

Consider the two points A(x1, y1) and B(x2, y2) on the coordinate plane.

The distance between the points A and B is

Distance d =

**3. Mid point**

Consider the two points A(x1, y1) and B(x2, y2) on the coordinate plane.

The coordinates of mid-point of the line segment joining the points A and B is

Mid-point M =

**4. Gradient or Slope**

Consider the two points A(x1, y1) and B(x2, y2) on the coordinate plane.

The gradient or slope of the line pass through the points A and B is

Gradient m =