Finding the components of a vector

find the components of vector a B so they're talking about the components at least in this context they're talking about breaking it down into if we start at point a and we're finishing at point B how much do we have to move in the x-direction so this is going to be essentially our change in X and then how much do we have to move in the y-direction to go from point A to point B so this one over here is going to be our change in X I just wrote the Greek letter Delta for change in X and then the second component is going to be our change in Y and to think about that let's just think about what our starting and final points our initial and our terminal point are so this point right over here point a its coordinates are 4 comma 4 and then point B its coordinates are let's see its x-coordinate is negative 7 comma negative 8 so let's first think about what our change in X is and like always I encourage you to pause the video and try to work through it on your own well let's see if we're starting at 4 and then we are we're going from x equals 4 that's what we're starting to x equals negative 7 so that right over there is our change in X and there's a couple of ways you could compute that you could say look we we finished at negative 7 we started at negative 4 you take your final point or you're where you end up so that's negative 7 and you subtract your initial point minus 4 which is going to be equal to negative 11 the negative tells us that we decreased in X by 11 and you could see that if you can you could just visually count the squares you could say look if I'm going from 4 to negative 7 have to go down 4 just to get back to x equals 0 and then I have to go down another 7 so I have to go to the left 11 spaces so that's negative 11 so that's my X component negative 11 and what is my change in Y well I'm going from y equals 4 in fact I'll start at this point right over here I'm starting at y equals 4 and I'm ending up at Y is equal to that other color so I'm starting at Y is equal to four and I'm ending up at Y is equal to negative eight so our change in Y our change in Y well it's going to be my final Y value which is negative eight - my initial Y value which is 4 minus 4 which is equal to negative 12 so negative 12 and you could see that here if I'm starting up you have to go four down just to get back to the x-axis that I have to go down another eight so I have to go down a total of 12 and you could see something interesting that I'm just set up here you could also view this you could view this this bigger vector vector a B is being constructed of this X this vector that goes purely in the X direction and this vector that goes purely in the Y direction if you were to add this red vector to this blue green dark blue green vector you would get vector a B but we'll talk more about that in future videos