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:

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