Problem: Which of the following methods of proving a geometric figure a locus is not correct?
Answer Choices:
A. Every point on the locus satisfies the conditions and every point not on the locus does not satisfy the conditions.
B. Every point not satisfying the conditions is not on the locus and every point on the locus does satisfy the conditions.
C. Every point satisfying the conditions is on the locus and every point on the locus satisfies the conditions.
D. Every point not on the locus does not satisfy the conditions and every point not satisfying the conditions is not on the locus.
E. Every point satisfying the conditions is on the locus and every point not satisfying the conditions is not on the locus.
Solution:
To prove that a geometric figure is a locus it is essential to (1) include all proper points, and (2) exclude all improper points. By this criterion, (B) is insufficient to guarantee condition (1); i.e., (B) does not say that every point satisfying the conditions lies on the locus.