The distance of the point (-12,5) from the origin is

Options

A. 12
B. 5
C. 13
D. 169

Answer

To find the distance of the point (-12, 5) from the origin (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
Here, the coordinates of the origin are \((x_1, y_1) = (0, 0)\) and the coordinates of the point are \((x_2, y_2) = (-12, 5)\).

### Step 2: Substitute the coordinates into the distance formula
Now, we substitute the coordinates into the distance formula:

\[ d = \sqrt{((-12) - 0)^2 + (5 - 0)^2} \]

### Step 3: Simplify the expression
This simplifies to:

\[ d = \sqrt{(-12)^2 + (5)^2} \]

### Step 4: Calculate the squares
Calculating the squares gives us:

\[ d = \sqrt{144 + 25} \]

### Step 5: Add the results
Now, we add the two values:

\[ d = \sqrt{169} \]

### Step 6: Find the square root
Taking the square root gives us:

\[ d = 13 \]

Thus, the distance of the point (-12, 5) from the origin is **13**.