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 =