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Determine the range of β for which the point (0, β) is located on or within the triangle formed by the equations y + 3x + 2 = 0, 3y − 2x − 5 = 0, and 4y − x − 14 = 0.
- 5 ≤ β ≤ 7
- 1/2 ≤ β ≤ 1
- 5/3 ≤ β ≤ 7/2
- None of these
Correct answer: 5/3 ≤ β ≤ 7/2
Solution
The triangle has vertices (-1,1),(-1.69,3.08),(4.4,4.6). On the line x=0, points inside the triangle lie between y=5/3 (from 3y-2x-5=0) and y=7/2 (from 4y-x-14=0). So 5/3 <= beta <= 7/2 (idx 2); stored '5<=beta<=7' is wrong.
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