n Learning and Teaching Mathematics - All cubic polynomials are point symmetric

Volume 2004, Issue 1
  • ISSN : 1990-6811


For instance, a graph is considered point symmetrical in relation to the origin when each point P of a graph, as shown in Figure I, has a corresponding point (also on the graph) under a reflection through so that . Or equivalently in the plane, each point P of the graph can be mapped onto a corresponding point (also on the graph) by means of a half-turn (a rotation through 180 degrees) around . Using the transformation formula for a half turn, it therefore follows that a graph is point symmetric in relation to the origin if ; in other words if it remains invariant under a half-turn around the origin.

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