The Midpoint and The Gradient or Slope of a Line Joining Two Points

         A Point which divides a line in to two equal parts is called mid point. The midpoint of the line joining the points (x₁, y₁) and (x₂, y₂) is calculated by the following formula:

                                   

Example:

Find the coordinates of the midpoint of the line joining (1, 2) and (3, 1).

The gradient of the line joining the points (x₁, y₁) and (x₂, y₂) is:

 

Example

Find the gradient of the line joining the points (5, 3) and (1, 4).

                                      

                         

Note: 

i. Slope of a horizontal line is zero.

ii. Slope of a vertical line is infinity or undefined.

 By: Sir Baqir

Distance Between any two Points

      The length of the line joining the points (x₁, y₁) and (x₂, y₂) or shortest distance between these two points, and is it is calculated by the formula given below:

Example:
Find the distance between the points (3, 5) and (2, 4).
(So in this case, x₂ = 2, x₁ = 3, y₂ = 4 and y₁ = 5).

                                                                                By: Sir Baqir Ali