If distance between the point (x, 2) and (3, 4) is 2, then find the value of x.
(a)3
(b)4
(c)2
(d)1

Answer

To solve the problem of finding the value of \( x \) such that the distance between the points \( (x, 2) \) and \( (3, 4) \) is equal to 2, we can follow these steps:

### Step 1: Use the Distance Formula
The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In our case, the points are \( (x, 2) \) and \( (3, 4) \). Thus, we can substitute:
- \( x_1 = x \)
- \( y_1 = 2 \)
- \( x_2 = 3 \)
- \( y_2 = 4 \)

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

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

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

### Step 5: Isolate the Squared Term
Subtract 4 from both sides:
\[ (3 - x)^2 = 0 \]

### Step 6: Solve for \( x \)
Taking the square root of both sides gives:
\[ 3 - x = 0 \]
Thus, solving for \( x \):
\[ x = 3 \]

### Conclusion
The value of \( x \) is \( 3 \). Therefore, the correct answer is:
\[ \text{(a) } 3 \]