If distance between the point (x, 2) and (3, 4) is 2, then the value of x =

Options

A. 0
B. 2
C. 3
D. 4

Answer

To solve the problem, we need to find the value of \( x \) such that the distance between the points \( (x, 2) \) and \( (3, 4) \) is equal to 2. We will use the distance formula to do this.

### Step-by-Step Solution:

1. **Identify the Points**:
- Let point A be \( (x, 2) \) and point B be \( (3, 4) \).

2. **Use the Distance Formula**:
The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \( (x_1, y_1) = (x, 2) \) and \( (x_2, y_2) = (3, 4) \).

3. **Set Up the Equation**:
According to the problem, the distance is 2, so we set up the equation:
\[ 2 = \sqrt{(3 - x)^2 + (4 - 2)^2} \]

4. **Simplify the Equation**:
First, calculate \( (4 - 2)^2 \):
\[ (4 - 2)^2 = 2^2 = 4 \]
Now substitute this back into the equation:
\[ 2 = \sqrt{(3 - x)^2 + 4} \]

5. **Square Both Sides**:
To eliminate the square root, square both sides:
\[ 2^2 = (3 - x)^2 + 4 \]
This simplifies to:
\[ 4 = (3 - x)^2 + 4 \]

6. **Isolate the Squared Term**:
Subtract 4 from both sides:
\[ 0 = (3 - x)^2 \]

7. **Solve for \( x \)**:
Taking the square root of both sides gives:
\[ 3 - x = 0 \]
Therefore, solving for \( x \):
\[ x = 3 \]

### Conclusion:
The value of \( x \) is \( 3 \).