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Answer: Choice D. (3j, 3k) and (3/j, 3/k)</h3>
The slash indicates a fraction.
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Proof:
We'll need to consider 4 different cases.
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Case (1): j > 0 and k > 0
If j > 0, then 3j > 0 and 3/j > 0
If k > 0, then 3k > 0 and 3/k > 0
The two points (3j, 3k) and (3/j, 3/k) are both in quadrant 1.
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Case (2): j > 0 and k < 0
If j > 0, then 3j > 0 and 3/j > 0
If k < 0, then 3k < 0 and 3/k < 0
Points (3j, 3k) and (3/j, 3/k) are both in quadrant 4.
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Case (3): j < 0 and k > 0
If j < 0, then 3j < 0 and 3/j < 0
If k > 0, then 3k > 0 and 3/k > 0
Points (3j, 3k) and (3/j, 3/k) are in quadrant 3.
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Case (4): j < 0 and k < 0
If j < 0, then 3j < 0 and 3/j < 0
If k < 0, then 3k < 0 and 3/k < 0
Points (3j, 3k) and (3/j, 3/k) are in quadrant 4.
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For nonzero integers j and k, we've shown that Points (3j, 3k) and (3/j, 3/k) are in the same quadrant. This concludes the proof.
