<p>The points (2, 1) and (-3, 5) lie along the line \(3x - 2y + 1 = 0\) on which side?</p>
Step-by-Step Solution
Key Concept: Two points lie on opposite sides of a line if substituting their coordinates into the line equation gives values with opposite signs. If both values have the same sign, the points lie on the same side.
<p><strong>Step 1:</strong> Let $l = 3x - 2y + 1$</p><p><strong>Step 2:</strong> Evaluate $l$ at point (2, 1): $l_1 = 3(2) - 2(1) + 1 = 6 - 2 + 1 = 5 > 0$</p><p><strong>Step 3:</strong> Evaluate $l$ at point (-3, 5): $l_2 = 3(-3) - 2(5) + 1 = -9 - 10 + 1 = -18 < 0$</p><p><strong>Step 4:</strong> Since $l_1 > 0$ and $l_2 < 0$, the values have opposite signs, meaning the two points lie on opposite sides of the line.</p><p>∴ Answer is (b) opposite side</p>
Correct Answer: B