The distance of point `A(-5,6)` from the origin is :

Options

A. `11` units
B. `61` units
C. `sqrt(11)` units
D. `sqrt(61)` units `1`

Answer

To find the distance of point \( A(-5, 6) \) 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 1: Identify the coordinates
The coordinates of the origin \( O \) are \( (0, 0) \) and the coordinates of point \( A \) are \( (-5, 6) \).

### Step 2: Substitute the coordinates into the distance formula
Here, \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (-5, 6) \). Plugging these values into the formula, we have:

\[ d = \sqrt{((-5) - 0)^2 + (6 - 0)^2} \]

### Step 3: Simplify the expression
Now, calculate the squares:

\[ d = \sqrt{(-5)^2 + (6)^2} \]

Calculating the squares gives:

\[ d = \sqrt{25 + 36} \]

### Step 4: Add the results
Now, add the results:

\[ d = \sqrt{61} \]

### Step 5: Final answer
Thus, the distance of point \( A(-5, 6) \) from the origin is:

\[ d = \sqrt{61} \text{ units} \]

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