# Exploring Coordinates and Vectors

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.

### René Descartes and the Fly on the Ceiling

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

### Coordinates of Corners

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

### Are We Nearly There?

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

### Vectors Round a Square

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

### Exploring Diagonals

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

### Areas from Vectors

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

### Dotty Grids Resources

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