Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
A Tilted Square
Stage: 4 Challenge Level:
Why do this problem?
The problem gives (a,b) and (c,d) as the opposite vertices of a
square and asks for the coordinates of the other two vertices. An
interactivity leads learners through a succession of tasks so that
they construct several squares for themselves that are 'tilted'
(i.e.edges not parallel to the axes) and explore the reasons that
the shapes they have drawn are actually squares.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.