# Co-ordinate Geometry

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

#### 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 =