To find the length of [tex]\( AB \)[/tex] given two points, [tex]\( A = (0, 0) \)[/tex] and [tex]\( B = (6, 3) \)[/tex], we will use the distance formula. The distance formula between two points [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] is given by:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Here, [tex]\( (x_1, y_1) = (0,0) \)[/tex] and [tex]\( (x_2, y_2) = (6,3) \)[/tex].
Plugging in these coordinates:
[tex]\[
d = \sqrt{(6 - 0)^2 + (3 - 0)^2}
\][/tex]
First, calculate the differences:
[tex]\[
6 - 0 = 6 \quad \text{and} \quad 3 - 0 = 3
\][/tex]
Next, square these differences:
[tex]\[
6^2 = 36 \quad \text{and} \quad 3^2 = 9
\][/tex]
Add these squares together:
[tex]\[
36 + 9 = 45
\][/tex]
Finally, take the square root of the sum:
[tex]\[
d = \sqrt{45} = \sqrt{9 \times 5} = 3 \sqrt{5} \approx 6.708
\][/tex]
Thus, the length of [tex]\( AB \)[/tex] is approximately 6.71 units.
So, the correct answer is:
B. 6.71 units
