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Proving a Locus

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February 1, 2009

Problem Statement

Which of the following methods of proving a geometric figure a locus is not correct? <spanclass=′latex−bold′>(A)</span> Every point of the locus satisfies the conditions and every point not on the locus does not satisfy the conditions. <span class='latex-bold'>(A)</span>\ \text{Every point of the locus satisfies the conditions and every point not on the locus does not satisfy the conditions.} <spanclass=′latex−bold′>(B)</span> Every point not satisfying the conditions is not on the locus and every point on the locus does satisfy the conditions. <span class='latex-bold'>(B)</span>\ \text{Every point not satisfying the conditions is not on the locus and every point on the locus does satisfy the conditions.} <spanclass=′latex−bold′>(C)</span> Every point satisfying the conditions is on the locus and every point on the locus satisfies the conditions. <span class='latex-bold'>(C)</span>\ \text{Every point satisfying the conditions is on the locus and every point on the locus satisfies the conditions.} <spanclass=′latex−bold′>(D)</span> Every point not on the locus does not satisfy the conditions and every point not satisfyingthe conditions is not on the locus. <span class='latex-bold'>(D)</span>\ \text{Every point not on the locus does not satisfy the conditions and every point not satisfying} \\ \text{the conditions is not on the locus.} <spanclass=′latex−bold′>(E)</span> Every point satisfying the conditions is on the locus and every point not satisfying the conditions is not on the locus. <span class='latex-bold'>(E)</span>\ \text{Every point satisfying the conditions is on the locus and every point not satisfying the conditions is not on the locus.}
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