Learning Resources

Focus G: Tangent Properties in a Coordinate System

Test yourself (solution)

Given: Information as shown on the diagram.

Prove: Either that AB is or is not a tangent.

Proof: Since AB is a tangent at A iff AB is perpendicular to the radius, we first construct the radius and find the required slopes:

But 3/5 and -7/4 are not negative reciprocals of each other (their product does not equal -1). Therefore AB is not perpendicular to OA, the radius. Therefore AB is NOT a tangent.