Cambridge IGCSE Mathematics · Syllabus 0580 · 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 IGCSE Mathematics.
Questions students ask about Length and Midpoint
Do I have to memorise the formulas, or are they given?
You have to know them, on both routes. Cambridge prints a List of formulas on page 2 of every paper — one for Core Papers 1 and 3, a longer one for Extended Papers 2 and 4 — and neither list contains a single coordinate-geometry formula. The Extended list adds only the quadratic formula, the sine rule, the cosine rule and the area of a triangle. So the gradient rule, \(y=mx+c\) and the parallel condition must be known on the Core route, and the length and midpoint formulas and the perpendicular condition must be known on top of those on the Extended route. 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.