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DIstance

Added May 11, 2017 •

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okay welcome to the last video in our unit 13 right triangle family so we've been talking about right triangles and today what we're going to do is talk about distance in this video we will talk about how to find and calculate distances and actually we've already done that haven't way in the last video which was on right triangles in real life we calculated a distance it was the distance between the two points on a map and since there was a right triangle that situation you could use the Pythagorean theorem will we're going to do the one thing today except instead of so can we find the distance between two points on a graph yes we can and instead of an axe I'm going to call distance Addie for distance and we can calculate the distance between those two points even if they're diagonal from each other and he if it's kind of a crooked line so all we have to do to find the distance between those two points is use the right triangle between those two points notice that from -4 5 to 5, 5 you have to go to the right 9 and then you also have to go up 10 so  if you want to pause a video you can count the number of little box on the grid to make sure I did that right but basically that's all I did is I counted little boxes on the grid and when I did that since I went to the right and then straight up need a right angle which made a right triangle which means that to find the distance between any two points on a graph all I have to do is just sketch out a graph of the right track distances and then find the hypotenuse of that right triangle to find the straight distance between those two points basically what I'm saying we're going to use the Pythagorean theorem here so  and I'd say 9 squared + 10 squared equals c squared hopefully can see we got all that then we just have to finish it off what's 9 squared 81 what's 10 squared 100 and you add those together you get a hundred 81 and you got a ton clear that to get D so we're going to do the square root of 181 so the distance between those two red dots is about 13.5 not exactly 18.5 we had to round that irrational square root up or down a little bit but it's roughly 13.5 and you're going to have two rounds your answers when you do these problems as well alright so let's try another example just to make sure you got it if you were trying to find the distance between 2, 4 + -1, 0 here's what you would have to do you would plot those two points  and then you would make a triangle  and that's where you're going to have to start to do some meth so first you're going to figure out how far is this leg right here well you just count the boxes one two three so this is three and then how far is this 1 2 3 4 right so this is 400 guess what I already kind of know this is just a three four five right triangle but just to make sure that you get it I would do 3 squared plus 4 squared equals D Square D for distance or you could put H for hypotenuse or whatever you want and then I would just Square the three Square the four  atom together and we know what squared makes 25 but just to show you what we're doing here we're going to unsquare the 25 and get the distance this time is is there exactly 5 away from each other  alright so that's how you can find the distance between any two points on what I want you to do is try it on your own soap lot those two dots straight line between them but then make a right triangle to connect the two dots and use a squared B squared c squared all right now we did this problem just a second ago right  what I want to show you is that we can do it a different way  instead of using a graph to do that we're going to use something called the distance formula don't like drawing graphs out every time that you have to do this the distance formula is good news because it's a way to do it with just the numbers except look at that formula it's kind of scary huh well I'm going to show you that this formula is not as scary as it looks the ex 1 X2 y1 Y2 I really just symbols to represent the two of the four the negative one in the zero the AC / on the upper left corner of the screen  so the distance from meal isn't that bad alright the X1 is the first x coordinate if the x coordinate of the first point the X2 is II x coordinate it's the x coordinate second point so x 1 is 2 x 2 is -1 why one is the first y-coordinate and Y2 is the second y coordinate play that's not too bad so now what we're going to do is we're going to go ahead and plug those numbers in where they be long we said did the two goes here  the negative one goes here and then the first y-coordinate goes here and the second y-coordinate goes here so all I really have to do now is put those numbers in there so this one two  semi put 2 - wait what was x 200 x 2 was this one Zoom - -1 what happens when you do minus negative 100 yeah that becomes plus positive 1 this is really just three squared this whole stuff here well what am I going to put in for why one why one was the first y-coordinate - Y2 which is the second y coordinate oh I know it 4-0 is 4-0 is for but remember where squaring both of these so I'm going to put for squared here and it's the square root of this whole thing see that it's the square root of the whole thing so now what I have to do is go back and do 3 squared which is 9  do Force which is 16  add them together which is 25 and if this is starting to look a lot like what we did the first time found with a Pythagorean theorem it's supposed to because these were the same two points so the answer should come out the same and it does so the distance is 5 and you can use the distance formula to find that distance if you don't like drawing pictures on a graph every time personally I think the distance formula gets a little complicated but I'll show you an easier way to do this this part right here what's go backwards please technology problems this right here  of the distance formula is X1 - X2 will couldn't I just kind of go like this and do X1 - X2 - - -1 and then couldn't I do this part as well y1 - Y2 I'm just going to subtract here and do 4-0 which is for and then can't I just Square this one square this one add them up  and take the square root of that oh maybe that's an easier format to do this and that way you don't necessarily have to remember all of the X1 y1 X2 Y2 you can just name the two points up like this and then just subtract subtract square square and square I don't know if that makes sense at all I'm just trying to help maybe it doesn't make sense but you can finish this problem the same way we finished the problem before and you get the same either way and maybe after we all we've done all this scribbling and writing you're deciding that sketching out a little graph and making a little red triangle might be your best option but I to you to at least try this practice problem and I like you to at least try  the distance formula on this I'll give you a little hint the first step that I would do if I was doing this would be to put three, two down here  and then I would maybe do a little some you can see if you can get it from there alright that's a distance and hope you now see finding distances is related to right triangles

Uploaded by Jeff Marbut.

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DIstance

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