Find the point on x-axis which is equidistant from points A(-1, 0) and B(5, 0).

Explanation

To find the point on the x-axis that is equidistant from the points A(-1, 0) and B(5, 0), we can follow these steps:

### Step 1: Define the Point on the X-axis
Let the point P on the x-axis be represented as P(x, 0), where x is the x-coordinate we need to find.

### Step 2: Use the Distance Formula
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Since point P is equidistant from points A and B, we can set the distances PA and PB equal to each other:
\[ PA = PB \]

### Step 3: Calculate Distances PA and PB
1. **Distance PA** from P to A(-1, 0):
\[ PA = \sqrt{(x - (-1))^2 + (0 - 0)^2} = \sqrt{(x + 1)^2} = |x + 1| \]

2. **Distance PB** from P to B(5, 0):
\[ PB = \sqrt{(x - 5)^2 + (0 - 0)^2} = \sqrt{(x - 5)^2} = |x - 5| \]

### Step 4: Set the Distances Equal
Now, we set the two distances equal to each other:
\[ |x + 1| = |x - 5| \]

### Step 5: Solve the Absolute Value Equation
This equation can be solved by considering two cases:

**Case 1:** \( x + 1 = x - 5 \)
- This simplifies to:
\[ 1 = -5 \quad \text{(not possible)} \]

**Case 2:** \( x + 1 = -(x - 5) \)
- This simplifies to:
\[ x + 1 = -x + 5 \]
\[ 2x = 4 \quad \Rightarrow \quad x = 2 \]

### Step 6: Conclusion
Thus, the point P on the x-axis that is equidistant from points A and B is:
\[ P(2, 0) \]