To solve this problem, we'll follow these steps:
1. Identify the coordinates of points Y and Z:
- Coordinates of point Y: [tex]\( (5, 0) \)[/tex]
- Coordinates of point Z: [tex]\( (7, 6) \)[/tex]
2. Calculate the ordered pair representing [tex]\(\overrightarrow{Y Z}\)[/tex]:
To find the ordered pair, we subtract the coordinates of point Y from the coordinates of point Z:
[tex]\[
(7-5, 6-0) = (2, 6)
\][/tex]
3. Find the magnitude of [tex]\(\overrightarrow{Y Z}\)[/tex]:
The magnitude of a vector [tex]\((a, b)\)[/tex] is given by the formula:
[tex]\[
\sqrt{a^2 + b^2}
\][/tex]
For our vector [tex]\((2, 6)\)[/tex], the magnitude is:
[tex]\[
\sqrt{2^2 + 6^2} = \sqrt{4 + 36} = \sqrt{40} = 2 \sqrt{10}
\][/tex]
Thus, the best answer that matches our calculations and the provided options is:
b. [tex]\((2, 6); 2 \sqrt{10}\)[/tex] units
So the correct choice is:
B
