smc

geometry senior

Problem

Which of the following methods of proving a geometric figure a locus is not correct?

(A)

Every point of 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.

Solution

Statement

Every point not satisfying the conditions is not on the locus and every point on the locus does satisfy the conditions.

is wrong because it does not imply that all points that satisfy the conditions are on the locus.

Final answer