Cambridge O Level Additional Mathematics · Syllabus 4037 · Straight-Line Graphs
Midpoint and Length of a Line Segment
What is Midpoint and Length of a Line Segment?
The midpoint of the segment joining two points is the point whose coordinates are the averages of the corresponding coordinates of the endpoints, given by the pair consisting of half the sum of the x-coordinates and half the sum of the y-coordinates. The length of the segment is the distance between the endpoints, obtained by applying Pythagoras to the horizontal and vertical differences, so it equals the square root of the sum of the squares of those differences. The length is always positive and is unaffected by the order in which the endpoints are taken, because each difference is squared. It is normally left as an exact surd in simplest form rather than rounded to a decimal.
This definition is part of the Straight-Line Graphs chapter in Cambridge O Level Additional Mathematics.