SM2.2 Coordinate geometry
You can find the distance between two points, the point dividing a segment in a given ratio, and the midpoint, and use these to reason about figures placed on a grid.
Topics shown in module order.
Coordinates turn geometry into arithmetic: a point becomes a pair of numbers, and questions about lengths and positions become calculations. The distance formula is the Pythagoras theorem wearing coordinates, and the section formula finds the point that splits a segment in any ratio, with the midpoint as its simplest case. This is the chapter where algebra and geometry stop being separate subjects, and everything from graphs to physics leans on it later.
Work through these
Find distances between pairs of points, and draw one small right triangle to see the formula as Pythagoras
One sketch, with the horizontal and vertical differences as legs, is worth more than the formula memorised cold. After it, the formula cannot be misremembered because it can be rebuilt.
Use the distance formula to show a triangle is isosceles or right angled from its vertices alone
Classifying a figure nobody drew is the chapter's characteristic question. It rewards the habit of computing all three sides before concluding anything, which is also the habit that catches errors.
Use the section formula to find a dividing point, and the midpoint formula as its special case
Seeing the midpoint as the section formula with a one-to-one ratio halves what there is to memorise. The awkward part is keeping the ratio's order straight, and doing a handful with a sketch settles it.
Given three vertices of a parallelogram, find the fourth using midpoints of diagonals
The diagonals of a parallelogram share a midpoint, and that one fact plus the midpoint formula finds the missing corner. It is the neatest example of a geometric property becoming two short equations.
Practice you have recorded
Optional, and yours. This records that you say you worked on this topic. It is not a check of whether you got anything right.
Sign in free to record your practice and keep it if you change phones.
Sign in to keep your progress.
Free resources
We haven't checked most of these for screen reader use yet.
Links last checked 7 Sept 2026.
Stuck here?
Ask a mentor. A real person answers, and they can see exactly which topic you're on. Usually within a couple of working days.
Checking your session…