The half plane represented by 4x+3y> 14 contains the point

Options

A. (0,0)
B. (2,2)
C. (3,4)
D. (1,1)

Answer

To determine which point lies in the half-plane represented by the inequality \(4x + 3y > 14\), we will evaluate each given point by substituting the coordinates into the inequality.

### Step-by-Step Solution:

1. **Identify the inequality**: We have the inequality \(4x + 3y > 14\).

2. **Evaluate each option**:
- **Option 1**: Point (0, 0)
\[ 4(0) + 3(0) > 14 \implies 0 > 14 \quad \text{(False)} \]
- **Option 2**: Point (2, 2)
\[ 4(2) + 3(2) > 14 \implies 8 + 6 > 14 \implies 14 > 14 \quad \text{(False)} \]
- **Option 3**: Point (3, 4)
\[ 4(3) + 3(4) > 14 \implies 12 + 12 > 14 \implies 24 > 14 \quad \text{(True)} \]
- **Option 4**: Point (1, 1)
\[ 4(1) + 3(1) > 14 \implies 4 + 3 > 14 \implies 7 > 14 \quad \text{(False)} \]

3. **Conclusion**: The only point that satisfies the inequality \(4x + 3y > 14\) is **Option 3: (3, 4)**.