Coordinates
by the Shropshire Mathematics Centre
The coordinate grid system offers a means of superimposing an order onto space. The
implications of grids based on other regular tessellating shapes may be worthwhile
exploring with pupils in addition to the conventional integer square version.
However, there seems to be ample scope for pupils to unearth and establish
interesting results based on the normal square grid system.
Properties can be derived from an exploration of arrangements of coordinates on
square dot lattice paper for:

Parallel lines (what property do the coordinates of points on parallel lines have?);

Right-angles (how can you work out that two lines are perpendicular from two
pairs of coordinates?);

Gradients (what is special about a straight line?);

Properties of quadrilaterals (how do you determine whether or not a shape is a
parallelogram from four given coordinates?);

Equal lengths (how can you tell that two distances between points are equal in
length or not?);

Symmetry (create a polygon with x = 3 as a line of symmetry);

Reflections in various lines (what happens if you reflect a point in x + y = 5?);

Dividing a line in a given ratio (give several pairs of points that have (4, 3) as a
mid-point, generalise; if (4, 3) is the centre of a square suggest possibilities for the
four coordinates of the corners);

Transformations (what happens to a shape if the second coordinate is doubled?);

Enlargements (draw a shape and a larger version of it—are there any relationships
between the coordinates?);

Vectors and much more