Coordinates and vectors are very useful tools for working out properties of lines and shapes drawn on a dotty grid. Have a look at the problems and see how you can use these tools to understand what's going on.

The coordinate system we commonly use is named after the French mathematician René Descartes, and was (allegedly) inspired by a fly on the ceiling.

Can you find a quick way to determine whether four coordinates are the corners of a square?

Try to visualise the route taken by the arrows in our animation. What patterns do you notice?

Explore the properties of vectors and find out what happens when you use them to describe a journey round a square.

Play with the interactivity and see what you notice. What interesting questions are there to ask about the diagonals of rectangles?

A parallelogram can be defined by two vectors. Can you discover a relationship between the two vectors and the area of the parallelogram?

Here are some resources to help you explore dotty grids, including some printable grids and an interactive environment.