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 = (y2 − y1)2 + (x2 − x1)2
Taking square root of both sides gives the formula for the distance (d) between two points.
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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:
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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:
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The gradient of a line can also be found if the angle it makes with the positive x-axis is known.
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From the diagram:
This formula also applies when x is bigger than 90°. The tangent and the gradient will be negative. |
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