One of the hardest coordinate proofs my students have come across is proving whether a given point does or does not lie on a circle with a given center. To start their exploration, we look at circles centered at the origin because they can easily count the length of the radius. In this activity, the strategy on how to perform the proof is described and an example proof is worked out step-by-step. Students follow a three step process to perform the proof (determine the length of the radius of the circle, determine the distance from the center to the point in question and compare the two distances to determine if the point lies on the circle). Student should already have been introduced to the distance formula to do these proofs.
*Note: this activity focuses only on circles centered at the origin and, therefore, is more of an introductory activity to be used before introducing proofs using circles that are not centered on the origin
A key is provided.