The distance of a point `(alpha, beta)` from the origin is ....

Options

A. `beta`
B. ` |beta|`
C. `|beta|+ |gamma|`
D. `sqrt(a ^(2) + beta^(2))`

Answer

To find the distance of the point \((\alpha, \beta)\) from the origin \((0, 0)\), we can use the distance formula derived from the Pythagorean theorem.

### Step-by-Step Solution:

1. **Identify the Points**:
- We have the point \(P(\alpha, \beta)\) and the origin \(O(0, 0)\).

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

3. **Substitute the Coordinates**:
- Here, we substitute \(x_1 = 0\), \(y_1 = 0\), \(x_2 = \alpha\), and \(y_2 = \beta\):
\[ d = \sqrt{(\alpha - 0)^2 + (\beta - 0)^2} \]

4. **Simplify the Expression**:
- This simplifies to:
\[ d = \sqrt{\alpha^2 + \beta^2} \]

5. **Conclusion**:
- Therefore, the distance of the point \((\alpha, \beta)\) from the origin is:
\[ \sqrt{\alpha^2 + \beta^2} \]