The distance of the point `P(-6,8)` from the origin is

Options

A. `8`
B. `2sqrt(7)`
C. `6`
D. `10`

Explanation

To find the distance of the point \( P(-6, 8) \) from the origin \( O(0, 0) \), we will 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 \( O \) has coordinates \( (0, 0) \).
- The point \( P \) has coordinates \( (-6, 8) \).

2. **Assign the coordinates**:
- Let \( (x_1, y_1) = (0, 0) \) (coordinates of the origin).
- Let \( (x_2, y_2) = (-6, 8) \) (coordinates of point P).

3. **Substitute the values into the distance formula**:
\[ d = \sqrt{((-6) - 0)^2 + (8 - 0)^2} \]

4. **Calculate the differences**:
- \( x_2 - x_1 = -6 - 0 = -6 \)
- \( y_2 - y_1 = 8 - 0 = 8 \)

5. **Square the differences**:
\[ d = \sqrt{(-6)^2 + (8)^2} \]
\[ d = \sqrt{36 + 64} \]

6. **Add the squares**:
\[ d = \sqrt{100} \]

7. **Take the square root**:
\[ d = 10 \]

### Final Answer:
The distance of the point \( P(-6, 8) \) from the origin is \( 10 \) units.