If two points on the number plane are joined a line is formed. Several properties of this line can be found:

Click Here for practice at calculating these three properties.

A line is drawn between the two points A and B

### The length of a line

The distance between two points on a number plane can be found using Pythagoras' Theorem.

From the diagram above, using Pythagoras' Theorem:

(Length of AB)^{2} = AC ^{2} + BC ^{2}

(Length of AB)^{2} = (y_{2} − y_{1})^{2} + (x_{2} − x_{1})^{2}

Taking square root of both sides gives the formula for the distance (d) between two points.

Click here to see an example.

### The mid-point of a line

The coordinates of the mid-point of the line AB can be found by finding the mid-point of BC and the mid-point of AC.

Mid-point of BC =

Mid-point of AC =

For the diagram above the mid-point of the line joining two points is given by:

Click here to see an example.

### The gradient of a line

The gradient of a line is a measure of how steep it is.

From earlier work, the gradient is given as:

For the diagram above the gradient of the line joining two points is given by:

Click here to see an example.

The gradient of a line can also be found if the angle it makes with the **positive** x-axis is known.

From the diagram:
This formula also applies when x is bigger than 90 The tangent and the gradient will be negative. |

Click here to see an example.