The distance of the point `P(3, -4)` from the origin is

Options

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

Explanation

To find the distance of the point \( P(3, -4) \) 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 1: Identify the coordinates
Let the coordinates of point \( P \) be \( (x_1, y_1) = (3, -4) \) and the coordinates of the origin \( O \) be \( (x_2, y_2) = (0, 0) \).

### Step 2: Substitute the coordinates into the distance formula
Substituting the coordinates into the distance formula:

\[ d = \sqrt{(0 - 3)^2 + (0 - (-4))^2} \]

### Step 3: Simplify the expression
Now simplify the expression:

\[ d = \sqrt{(-3)^2 + (0 + 4)^2} \]
\[ d = \sqrt{9 + 16} \]

### Step 4: Calculate the sum inside the square root
Now calculate the sum:

\[ d = \sqrt{25} \]

### Step 5: Find the square root
Finally, find the square root:

\[ d = 5 \]

Thus, the distance of the point \( P(3, -4) \) from the origin is \( 5 \) units.