The distance of point `(5, -7)` from origin is :

Options

A. `sqrt(74)`
B. `-2`
C. 2
D. 12

Answer

To find the distance of the point \( (5, -7) \) from the origin \( (0, 0) \), 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-by-Step Solution:

1. **Identify the coordinates**:
- The point \( A \) is \( (5, -7) \) and the origin \( O \) is \( (0, 0) \).
- Here, \( (x_1, y_1) = (5, -7) \) and \( (x_2, y_2) = (0, 0) \).

2. **Apply the distance formula**:
\[ d = \sqrt{(0 - 5)^2 + (0 - (-7))^2} \]

3. **Calculate the differences**:
- \( x_2 - x_1 = 0 - 5 = -5 \)
- \( y_2 - y_1 = 0 - (-7) = 0 + 7 = 7 \)

4. **Square the differences**:
\[ d = \sqrt{(-5)^2 + (7)^2} \]
\[ d = \sqrt{25 + 49} \]

5. **Add the squares**:
\[ d = \sqrt{74} \]

6. **Final answer**:
The distance of the point \( (5, -7) \) from the origin is \( \sqrt{74} \).