A translation is a movement of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. The graph of \(y = f(x)\) where \(f(x) = x^2\) is the same as the ...

A translation is a movement of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. The graph of \(f(x) = x^2\) is the same as the graph of \(y = x^2\).

Two kinds of extensions to David Lewin's transformation theory are proposed. First, cross-type transformations transform one sort of object to another: for instance, mappings from triads to seventh ...

Materials were written for an entire year's course in geometry in which transformations were used to develop the concepts of congruence, similarity, and symmetry, as well as being a vehicle for proof.