The distance of the `B(6,6)` from the origin is:

Options

A. ` sqrt(53)` units
B. ` sqrt(41) ` units
C. ` sqrt( 72)` units
D. `sqrt(145)` units

Answer

To find the distance of the point \( B(6,6) \) 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
Here, the coordinates of the origin \( O \) are \( (0, 0) \) and the coordinates of point \( B \) are \( (6, 6) \).

### Step 2: Substitute the coordinates into the distance formula
We will substitute \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (6, 6) \) into the distance formula:

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

### Step 3: Simplify the expression
Now, we simplify the expression inside the square root:

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

Calculating the squares:

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

### Step 4: Add the values
Now, we add the values:

\[ d = \sqrt{72} \]

### Step 5: Simplify the square root
We can simplify \( \sqrt{72} \):

\[ \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2} \]

### Final Result
Thus, the distance of point \( B(6,6) \) from the origin \( O(0,0) \) is:

\[ d = 6\sqrt{2} \text{ units} \]

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