Discussion
Which of the following points lies on the same side as the origin, with reference to the line \(3x + 7y = 2\) ?
Answer: D
The point (0.5, 0) lies on the same side of the line as the origin. At the origin, \(3x + 7y = 0\), which is less than 2. For each point, evaluate \(3x + 7y\):
\[ (3, 0): 9 \gt 2 \qquad (1, 0): 3 \gt 2 \]
\[ (0.5, 0.5): 5 \gt 2 \qquad (0.5, 0): 1.5 \lt 2 \]
Only (0.5, 0) gives a value below 2, the same sign of difference as the origin.
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