Write the ordered pair that represents [tex]$\overrightarrow{YZ}$[/tex]. Then find the magnitude of [tex]$\overrightarrow{YZ}$[/tex].

Given:
[tex]$Y(5, 0)$[/tex] and [tex]$Z(7, 6)$[/tex]

A. [tex]$(2, 6); \sqrt{12}$[/tex] units
B. [tex]$(2, 6); 2 \sqrt{10}$[/tex] units
C. [tex]$\{5, 6\}; \sqrt{12}$[/tex] units
D. [tex]$\{5.6\}; 2 \sqrt{10}$[/tex] units

Please select the best answer from the choices provided:
A, B, C, or D.



Answer :

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