Coordinates

problem
Isosceles triangles

Age

11 to 14

Challenge level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
problem
Cartesian isometric

Age

7 to 11

Challenge level

The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?
problem
Ten hidden squares

Age

7 to 14

Challenge level

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
problem
Fred the class robot

Age

7 to 11

Challenge level

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?
problem
3D treasure hunt

Age

14 to 18

Challenge level

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
problem
Something in common

Age

14 to 16

Challenge level

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
problem
Mesh

Age

16 to 18

Challenge level

A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?
problem
Coordinate patterns

Age

11 to 14

Challenge level

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
problem
A shade crossed

Age

14 to 16

Challenge level

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?
problem
Rational round

Age

16 to 18

Challenge level

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.