What is the distance of the point P(3, -4) from the origin?

Options

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

Answer

To find the distance of the point P(3, -4) from the origin O(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 coordinates:**
- The coordinates of the origin O are \( (x_1, y_1) = (0, 0) \).
- The coordinates of the point P are \( (x_2, y_2) = (3, -4) \).

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

3. **Simplify the expression:**
- Calculate \( (3 - 0)^2 \):
\[ (3 - 0)^2 = 3^2 = 9 \]
- Calculate \( (-4 - 0)^2 \):
\[ (-4 - 0)^2 = (-4)^2 = 16 \]

4. **Add the squared values:**
\[ d = \sqrt{9 + 16} = \sqrt{25} \]

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

### Final Answer:
The distance of the point P(3, -4) from the origin is **5 units**.

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