To find the length of the line segment between points [tex]\(A = (0, 0)\)[/tex] and [tex]\(B = (6, 3)\)[/tex], we use the distance formula, which is defined as:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Here, [tex]\(A = (x_1, y_1)\)[/tex] and [tex]\(B = (x_2, y_2)\)[/tex]. Substituting the given coordinates:
[tex]\[
d = \sqrt{(6 - 0)^2 + (3 - 0)^2}
\][/tex]
Simplify inside the square root:
[tex]\[
d = \sqrt{6^2 + 3^2}
\][/tex]
Calculate the squares:
[tex]\[
d = \sqrt{36 + 9}
\][/tex]
Add the values:
[tex]\[
d = \sqrt{45}
\][/tex]
Taking the square root of 45 gives us:
[tex]\[
d \approx 6.71
\][/tex]
Thus, the length of the line segment [tex]\(\overline{AB}\)[/tex] is approximately 6.71 units. Therefore, the correct answer is:
D. 6.71 units
