Question:
The point which lies in the half-plane $2x + y - 4 \le 0$ is:
The point which lies in the half-plane $2x + y - 4 \le 0$ is:
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Substitute point and check sign.
Updated On: Jul 1, 2025
- (0, 8)
- (1, 1)
- (5, 5)
- (2, 2)
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The Correct Option is B
Solution and Explanation
Plug points into $2x + y - 4$:
- (0, 8): $0 + 8 - 4 = 4$ (not $\le 0$)
- (1, 1): $2(1) + 1 - 4 = -1$ (OK)
- (5, 5): $10 + 5 - 4 = 11$ (not OK)
- (2, 2): $4 + 2 - 4 = 2$ (not OK)
So only (1, 1) works.
- (0, 8): $0 + 8 - 4 = 4$ (not $\le 0$)
- (1, 1): $2(1) + 1 - 4 = -1$ (OK)
- (5, 5): $10 + 5 - 4 = 11$ (not OK)
- (2, 2): $4 + 2 - 4 = 2$ (not OK)
So only (1, 1) works.
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