The Length, Midpoint and Gradient of a Line
Suppose we want to find the length of the line between A and B in the diagram below.
We draw a straight line between A and B, and make this rhe hypotenuse of a right angled triangle by drawing a horizontal line from A to a point directly below B and another line down from B to a point right of A. This produces the diagram below.
We now have a right angled triangle with base 9 and height 7.
Using Pythagoras theorem gives
The midpoint of the line AB is
The gradientof the line is the height of the triangle above divided by the base: