The point on x-axis which is equidistant from (-4, 0) and (10, 0) is:

Options

A. (7, 0)
B. (5, 0)
C. (0, 0)
D. (3, 0)

Answer

To find the point on the x-axis that is equidistant from the points (-4, 0) and (10, 0), we can follow these steps:

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

### Step 2: Use the distance formula
The distance from the point \( (a, 0) \) to the point \( (-4, 0) \) can be calculated using the distance formula:
\[ d_1 = \sqrt{(a - (-4))^2 + (0 - 0)^2} = \sqrt{(a + 4)^2} = |a + 4| \]

The distance from the point \( (a, 0) \) to the point \( (10, 0) \) is:
\[ d_2 = \sqrt{(a - 10)^2 + (0 - 0)^2} = \sqrt{(a - 10)^2} = |a - 10| \]

### Step 3: Set the distances equal
Since the point \( (a, 0) \) is equidistant from both points, we can set the distances equal to each other:
\[ |a + 4| = |a - 10| \]

### Step 4: Solve the equation
We will consider two cases based on the absolute value equation.

**Case 1:** \( a + 4 = a - 10 \)
\[ 4 = -10 \quad \text{(This is not possible)} \]

**Case 2:** \( a + 4 = -(a - 10) \)
\[ a + 4 = -a + 10 \]
\[ a + a = 10 - 4 \]
\[ 2a = 6 \]
\[ a = 3 \]

### Step 5: Conclusion
The point on the x-axis that is equidistant from the points (-4, 0) and (10, 0) is \( (3, 0) \).