The distance of point `(-4, 5)` from origin is :

Options

A. 1
B. 9
C. `sqrt(41)`
D. None of these

Answer

To find the distance of the point \((-4, 5)\) from the origin \((0, 0)\), 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 1: Identify the points
Here, we have:
- Point A (the given point): \((-4, 5)\) which means \(x_1 = -4\) and \(y_1 = 5\)
- Point B (the origin): \((0, 0)\) which means \(x_2 = 0\) and \(y_2 = 0\)

### Step 2: Substitute the values into the distance formula
Now, substituting the values into the distance formula:

\[ d = \sqrt{(0 - (-4))^2 + (0 - 5)^2} \]

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

\[ d = \sqrt{(0 + 4)^2 + (0 - 5)^2} \]
\[ d = \sqrt{4^2 + (-5)^2} \]
\[ d = \sqrt{16 + 25} \]

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

\[ d = \sqrt{41} \]

### Final Answer
Thus, the distance of the point \((-4, 5)\) from the origin is:

\[ \sqrt{41} \]

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