The question asks us to determine which quadrant (w, z) is in, given that neither w nor z is equal to 0. Note that points in quadrant I have positive x and y values, points in quadrant II have negative x values and positive y values, points in quadrant III have negative x and y values, and points in quadrant IV have positive x values and negative y values.
Statement 1 tells us that (z, w) is in quadrant III. As we just observed above, points in quadrant III have negative x values and negative y values, and therefore both w and z are negative and therefore (w, z) is also in quadrant III. Statement 1 alone is sufficient to answer the question. The answer is A or D.
Statement 2 tells us that (-w, z) is in quadrant IV. As we've said, all points in quadrant IV have positive x values and negative y values. This tells us that -w is positive and so w is negative, and that z is negative. Since w and z are both negative, (w, z) is in quadrant III. Statement 2 alone is also sufficient to answer the question.
Answer choice D is correct.
Regards,
Karthik
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