Points (1, 2) and (2, 1) are:

Options

A. On the same side of the line `4x+2y=1`
B. On the line `4x+2y=1`
C. On the opposite sides of `4x+2y=1`
D. None of these

Answer

To determine the position of the points (1, 2) and (2, 1) with respect to the line given by the equation \(4x + 2y = 1\), we will substitute each point into the equation and analyze the results.

### Step-by-Step Solution:

1. **Identify the Line Equation**:
The equation of the line is given as:
\[ 4x + 2y = 1 \]

2. **Substitute the First Point (1, 2)**:
Substitute \(x = 1\) and \(y = 2\) into the equation:
\[ 4(1) + 2(2) = 4 + 4 = 8 \]
Now, compare this to 1:
\[ 8 - 1 = 7 \quad (\text{which is } > 0) \]

3. **Substitute the Second Point (2, 1)**:
Substitute \(x = 2\) and \(y = 1\) into the equation:
\[ 4(2) + 2(1) = 8 + 2 = 10 \]
Now, compare this to 1:
\[ 10 - 1 = 9 \quad (\text{which is } > 0) \]

4. **Analyze the Results**:
- For the point (1, 2), the result is \(7 > 0\).
- For the point (2, 1), the result is \(9 > 0\).
Since both results are greater than 0, we conclude that both points lie on the same side of the line.

5. **Conclusion**:
The points (1, 2) and (2, 1) are on the same side of the line \(4x + 2y = 1\).

### Final Answer:
The points (1, 2) and (2, 1) are on the same side of the line.

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