Calculate the distance between A(5, -3) and B on the y-axis whose ordiate is 9.

Answer

To find the distance between the points A(5, -3) and B(0, 9) (where B lies on the y-axis), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Coordinates of Points A and B**:
- Point A is given as A(5, -3).
- Point B lies on the y-axis, which means its x-coordinate is 0. Since the ordinate (y-coordinate) is given as 9, we can write Point B as B(0, 9).

2. **Use the Distance Formula**:
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, we can assign:
- \(x_1 = 5\), \(y_1 = -3\) (for Point A)
- \(x_2 = 0\), \(y_2 = 9\) (for Point B)

3. **Substitute the Coordinates into the Formula**:
Substitute the values into the distance formula:
\[ d = \sqrt{(0 - 5)^2 + (9 - (-3))^2} \]

4. **Calculate the Differences**:
- Calculate \(0 - 5 = -5\)
- Calculate \(9 - (-3) = 9 + 3 = 12\)

5. **Square the Differences**:
- \((-5)^2 = 25\)
- \(12^2 = 144\)

6. **Add the Squares**:
\[ d = \sqrt{25 + 144} = \sqrt{169} \]

7. **Calculate the Square Root**:
\[ d = 13 \]

### Final Answer:
The distance between points A(5, -3) and B(0, 9) is **13 units**.

---