Education Technology

A Symmetric View of Tangent and Normal Lines to a Curve

Published on 05/09/2010

Activity Overview

In this activity students will make concept connections numerically, graphically and analytically concerning the relationship between tangent and normal lines to a curve and its inverse. Students examine the necessary condition for these lines to intersect to form a deltoid, a non-convex quadrilateral which has two pairs of adjacent equal sides.

Before the Activity

Prerequisite knowledge:

  • Content knowledge of the algebraic and geometric properties of finding tangent and normal lines at symmetry points on a differentiable function and its inverse
  • Calculator background in graphing tangents and normal lines to a curve
  • During the Activity

    Download the TNS file and make it available to students.