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in Mathematics by (79.8k points)

If (0, β) lies on or inside the triangle formed by the lines 3x + y + 2 = 0, 3y − 2x − 5 = 0 and 4y + x − 14 = 0, then

(1) 5/2 ≤ β ≤ 7/3

(2) 5/3 ≤ β ≤ 7/2

(3) 7/3 ≤ β ≤ 5/2

(4) none of these

1 Answer

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Best answer

Correct option (2) 5/3 ≤ β ≤ 7/2

Explanation: 

(0, β) is a point on y-axis. Solving the given equations, we get the vertices as A(− 2, 4), B (2, 3) and C( − 1, 1). The side AB i.e., 4y + x − 14 = 0

meets the y-axis at point P (0.7/2) and the side BC i.e., 3y − 2x − 5 = 0 

meets the y-axis at Q (0,5/3)

For the point (0, β) to lie on or inside the triangle, we must have 5/3 ≤ β ≤7/2.

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