Midpoint of a Line (Edexcel IGCSE Maths)

Spec point — 3.3E

Midpoint of a line

How do I find the midpoint of a line?

• The midpoint of a line will be the same distance from both endpoints
• You can think of a midpoint as being the average (mean) of two coordinates
• The midpoint of $( x_{1} , y_{1} )$ and $( x_{2} , y_{2} )$ is

$( \frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2} )$

Worked Example The coordinates of A are (−4, 3) and the coordinates of B are (8, −12).

Find the coordinates of the midpoint of AB.

Answer:

The midpoint can be found using $( \frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2} )$

Substitute in the values of x and y from each point into their correct positions

$( \frac{- 4 + 8}{2} , \frac{3 + - 12}{2} ) = ( \frac{4}{2} , \frac{- 9}{2} )$

Simplify

Final answer: (2, −4.5)