The distance of the point p(3,4) from the origin is

Options

A. 3
B. 4
C. 7
D. 5

Answer

To find the distance of the point P(3, 4) from the origin O(0, 0), we will use the distance formula. The distance formula between two points (x1, y1) and (x2, y2) is given by:

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

### Step-by-step Solution:

1. **Identify the coordinates of the points**:
- The coordinates of point P are (3, 4).
- The coordinates of the origin O are (0, 0).

2. **Assign the coordinates to the formula**:
- Let (x1, y1) = (0, 0) and (x2, y2) = (3, 4).

3. **Substitute the coordinates into the distance formula**:
\[ d = \sqrt{(3 - 0)^2 + (4 - 0)^2} \]

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

5. **Square the differences**:
\[ d = \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} \]

6. **Add the squares**:
\[ d = \sqrt{25} \]

7. **Take the square root**:
\[ d = 5 \]

### Conclusion:
The distance of the point P(3, 4) from the origin O(0, 0) is 5 units.

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