Calculate the distance between A (7,3) and B on the x-axis whose abscissa is 11.

Answer

To calculate the distance between the points A(7, 3) and B(11, 0), we can follow these steps:

### Step 1: Identify the coordinates of the points
- Point A is given as A(7, 3).
- Point B is on the x-axis with an abscissa of 11, so its coordinates are B(11, 0).

### Step 2: Use the distance formula
The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

### Step 3: Substitute the coordinates into the formula
Here, \( (x_1, y_1) = (7, 3) \) and \( (x_2, y_2) = (11, 0) \). Substituting these values into the distance formula:
\[ d = \sqrt{(11 - 7)^2 + (0 - 3)^2} \]

### Step 4: Simplify the expression
Calculate \( (11 - 7) \) and \( (0 - 3) \):
\[ d = \sqrt{(4)^2 + (-3)^2} \]
\[ d = \sqrt{16 + 9} \]

### Step 5: Final calculation
Now, add the squares:
\[ d = \sqrt{25} \]
\[ d = 5 \]

### Conclusion
The distance between points A(7, 3) and B(11, 0) is 5 units.

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