Answer:
Yes, vectors u and v are equal.
Step-by-step explanation:
We need to check whether vectors u and v are equal or not.
If the initial point is
and terminal point is
, then the vector is
![Vector=(x_2-x_1)i+(y_2-y_1)j](https://tex.z-dn.net/?f=Vector%3D%28x_2-x_1%29i%2B%28y_2-y_1%29j)
Vector v with an initial point of (-5,22) and a terminal point of (20,60).
![\overrightarrow v=(20-(-5))i+(60-22)j](https://tex.z-dn.net/?f=%5Coverrightarrow%20v%3D%2820-%28-5%29%29i%2B%2860-22%29j)
..... (1)
Vector u with an initial point of (50,120) and a terminal point of (75,158).
![\overrightarrow u=(75-50)i+(158-120)j](https://tex.z-dn.net/?f=%5Coverrightarrow%20u%3D%2875-50%29i%2B%28158-120%29j)
.... (2)
From (1) and (2) we get
![\overrightarrow u=\overrightarrow v](https://tex.z-dn.net/?f=%5Coverrightarrow%20u%3D%5Coverrightarrow%20v)
Therefore, vectors u and v are equal.
to get the the equation of any straight line, we only need two points off of it, let's use the two points already in the picture.
![(\stackrel{x_1}{2}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{2}}}\implies \cfrac{-10}{-2}\implies 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{5}(x-\stackrel{x_1}{2}) \\\\\\ y-10=5x-10\implies y=5x](https://tex.z-dn.net/?f=%28%5Cstackrel%7Bx_1%7D%7B2%7D~%2C~%5Cstackrel%7By_1%7D%7B10%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B0%7D~%2C~%5Cstackrel%7By_2%7D%7B0%7D%29%20~%5Chfill%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%20%7B%5Cstackrel%7By_2%7D%7B0%7D-%5Cstackrel%7By1%7D%7B10%7D%7D%7D%7B%5Cunderset%7Brun%7D%20%7B%5Cunderset%7Bx_2%7D%7B0%7D-%5Cunderset%7Bx_1%7D%7B2%7D%7D%7D%5Cimplies%20%5Ccfrac%7B-10%7D%7B-2%7D%5Cimplies%205%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%5Cimplies%20y-%5Cstackrel%7By_1%7D%7B10%7D%3D%5Cstackrel%7Bm%7D%7B5%7D%28x-%5Cstackrel%7Bx_1%7D%7B2%7D%29%20%5C%5C%5C%5C%5C%5C%20y-10%3D5x-10%5Cimplies%20y%3D5x)
16 is the correct answer to this problem
Answer:
c
Step-by-step explanation:
Reflection across the x-axis reverses the sign of the y-values
Answer:
14
Step-by-step explanation: