What is the distance between the points A (4,5) and B(2, 5) ?

Options

A. 4
B. 2
C. 16
D. `sqrt102`

Answer

To find the distance between the points A(4,5) and B(2,5), we can use the distance formula. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

### Step 1: Identify the coordinates
Here, we have:
- Point A: \( (x_1, y_1) = (4, 5) \)
- Point B: \( (x_2, y_2) = (2, 5) \)

### Step 2: Substitute the coordinates into the distance formula
Now, we substitute the coordinates into the distance formula:

\[ d = \sqrt{(2 - 4)^2 + (5 - 5)^2} \]

### Step 3: Calculate the differences
Calculate the differences:

\[ d = \sqrt{(-2)^2 + (0)^2} \]

### Step 4: Simplify the squares
Now, simplify the squares:

\[ d = \sqrt{4 + 0} \]

### Step 5: Calculate the square root
Finally, calculate the square root:

\[ d = \sqrt{4} = 2 \]

Thus, the distance between points A and B is \( 2 \).