Length of a Line (Cambridge (CIE) IGCSE International Maths)

Revision Note

Written by: Jamie Wood

Reviewed by: Dan Finlay

The distance between two points with coordinates $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ can be found using the formula

$d = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}}$

This formula uses Pythagoras’ theorem $a^{2} + b^{2} = c^{2}$
- It is applied to the difference in the $x$ -coordinates and the difference in the $y$ -coordinates

Be extra careful when negative coordinates are involved
- It can help to put negative numbers in brackets to make your working clearer
- E.g. $(- 6) - (- 8) = 2$

Point A has coordinates (3, -4) and point B has coordinates (-5, 2).

Calculate the distance of the line segment AB.

Using the formula for the distance between two points, $d = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}}$

Substitute in the two given coordinates

$d = \sqrt{{(3 - (- 5))}^{2} + {((- 4) - 2)}^{2}}$

Be careful with the negative numbers
$3 - (- 5) = 8$ and $(- 4) - 2 = - 6$

Simplify

$d = \sqrt{{(8)}^{2} + {(- 6)}^{2}} = \sqrt{64 + 36} = \sqrt{100} = 10$

10 units

Last updated: 5 June 2024

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