What is the distance of point `K(-4,8)` from the origin?

Options

A. 3 units
B. `4sqrt5` units
C. 7 units
D. 10 units

Answer

To find the distance of point K(-4, 8) from the origin (0, 0), we can use the distance formula, which is given by:

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

Where:
- \( (x_1, y_1) \) are the coordinates of the first point (the origin in this case).
- \( (x_2, y_2) \) are the coordinates of the second point (point K).

### Step-by-Step Solution:

1. **Identify the Coordinates**:
- The coordinates of the origin are \( (0, 0) \).
- The coordinates of point K are \( (-4, 8) \).

2. **Substitute the Coordinates into the Distance Formula**:
- Here, \( x_1 = 0 \), \( y_1 = 0 \), \( x_2 = -4 \), and \( y_2 = 8 \).
- Substitute these values into the formula:
\[ D = \sqrt{((-4) - 0)^2 + (8 - 0)^2} \]

3. **Calculate the Differences**:
- Calculate \( (-4) - 0 = -4 \).
- Calculate \( 8 - 0 = 8 \).

4. **Square the Differences**:
- Now square the differences:
\[ D = \sqrt{(-4)^2 + (8)^2} \]
- This becomes:
\[ D = \sqrt{16 + 64} \]

5. **Add the Squares**:
- Add the squared values:
\[ D = \sqrt{80} \]

6. **Simplify the Square Root**:
- The square root of 80 can be simplified:
\[ D = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5} \]

### Final Answer:
The distance of point K(-4, 8) from the origin is \( 4\sqrt{5} \) units.