I know this should be very easy but unfortunately I couldn't attend few of my classes and now I don't understand how to calculate.
This is the problem:
I am given two points: $A=(1,-1)$ and $B=(-4,5)$. I calculated $AB$'s length, it is $\sqrt{61}$.
I should extend $\overrightarrow{AB}$ vector to a point that my let's say $AC$'s length is $\sqrt{549}$ . I am really sorry if this is kinda gibberish, English isn't my main language, I know general English but not terms and such.
$$\overrightarrow{AB} = B - A= (b_1-a_1, b_2-a_2) = (-5,6)$$
$$\overrightarrow{AC} = k\cdot\overrightarrow{AB}= k\cdot(-5,6)=(-5k, 6k)$$
$$\left|\overrightarrow{AC}\right| = \Big|(5k, 6k)\Big| = \sqrt{(-5k)^2 + (6k)^2} = k\cdot\sqrt{61}$$
Now, you want $\left|\overrightarrow{AC}\right| = \sqrt{549},\ $ i. e.
$$k\cdot\sqrt{61} = \sqrt{549}$$
You will obtain $k = 3,$ so $$\overrightarrow{AC} = 3\cdot\overrightarrow{AB} = 3\cdot(-5,6)=(-15, 18)$$
and
$$\color{red}C = A + \overrightarrow{AC} = (1,-1) + (-15,18) =\color{red}{(-14, 17)}$$