Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Coordinate Geometry
Length and Midpoint
What is Length and Midpoint?
The length of a line segment joining two points is the square root of the sum of the squares of the horizontal and vertical changes between them, which is Pythagoras applied to the right-angled triangle whose hypotenuse is the segment; it is always non-negative. The midpoint of the segment is the point whose coordinates are the mean of the two x-coordinates and the mean of the two y-coordinates, and it lies exactly halfway along the segment.
This definition is part of the Coordinate Geometry chapter in Cambridge O Level Mathematics (Syllabus D).
Questions students ask about Length and Midpoint
Do I have to memorise the formulas, or are they given?
You have to know them. The gradient, length and midpoint formulas and the parallel and perpendicular conditions are not provided in the examination. The good news is that they all come from one picture: draw the gradient triangle between two points and the gradient is one side over the other, the length is the hypotenuse by Pythagoras, and the midpoint is halfway along both sides.