Find the distance of the point (7,-8)from the orgin

Answer

To find the distance of the point (7, -8) 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 Points**:
- The origin is the point \( (0, 0) \).
- The given point is \( (7, -8) \).

2. **Assign Coordinates**:
- Let \( (x_1, y_1) = (0, 0) \) (the origin).
- Let \( (x_2, y_2) = (7, -8) \).

3. **Substitute into the Distance Formula**:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates:
\[ d = \sqrt{(7 - 0)^2 + (-8 - 0)^2} \]

4. **Calculate the Differences**:
\[ d = \sqrt{(7)^2 + (-8)^2} \]

5. **Square the Differences**:
\[ d = \sqrt{49 + 64} \]

6. **Add the Squares**:
\[ d = \sqrt{113} \]

7. **Final Result**:
The distance of the point (7, -8) from the origin is:
\[ d = \sqrt{113} \text{ units} \]