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Section 5.2 (Median)

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5.2 Notes on Median explained and worked out by me.

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price of Jaguar going to talk about a triangle angle bisector of a segment which is a medium we already went over this in class but and I would go back again and try to explain it a little bit slower if you need to go back or what comedian is a line segment that starts at 8 perpendicular bisector that can come from anywhere like an angle bisector to the opposite side of the triangle it's going to go to lot ID and the meeting itself and what happened is when it goes from the vertex to the middle of the side so it's with that. can you see who is congruent to it does not have to hit at a right angle is not necessarily perpendicular to the segment it does not it does is literally by segments segment bisector of line 84 the definition of segment bisector it would be nice if they would be a median in there for 80 will be congruent to BD if we talked about the past when I see those words I would go ahead and I'll ride my finger when it says that a b so this second I'm here I'm going to put in as x -7 it does that ad is x + 3 he is 2x - 17 and they want to survive angry was he is not at all related to the parts that are actually the median. Or I can apply the next but again we're going to stop right here is congruent congruent congruent to CD which what exit is equal to 2x - 17 so when I add 17 / I get 20 x there for where is going to equal x -7 so when I played that in a bee is going to equal 20 - 713 plug it in here we did it this is 23 and this would be 40 - 17 which also is 23 guy told me that you look at that second right now the point of concurrency that goes with me as you can see different than the other in the center is at the centroid each line does go fully through the triangle so Big E L J comedian and if you notice what happens if they all beat up and it says that a point at which all the medians of a triangle intersect going to be two-thirds of the distance keep in mind you read this here 2/3 of the distance from the vertex talking about BL we're talking about that BP is 2/3 of DL 1/3 of the empire into a ratio of to Tokyo would have a 1 to 2 ratio to be so let's look at some examples I'm going to do one and then I want you to try to what kind of talk about what that's going to look like as well so for this particular problem I'm going to go to label everything it says that why Telecare why the entire line here it is 12 and it wants me to know what is YP and what is PV so what we see here is that why you shouldn't go to words of the entire line wives that looks like in terms of numbers so why he is going to be two thirds of 12 / 24 / 3 so Whitey is a V8 play the other one is wanted to talk for Speedy now we can do this one of two ways maybe we talked about earlier earlier ipv is going to be one third of the entire line why they so that means it equal to 1/3 12 OPB is in April for that we all could have thought about it unit we also could have thought about it in terms of the whole I was 12 while he was 8 then we can do just the track today from 12 and got are four units left over here or remember we said that's from the vertex to the Droid is going to be a 2 to 1 ratio so therefore we could have had what to get for a czar i unit there I don't want you to try the next couple this one said that at the entire line is 15 to one of my nefcu and QC so remember I was just like last time we see that it's going to be one third of 15 minute I line so ask you is going to equal 5 units staying is going to be set alarm 15 minutes so therefore is going to give you a shootout up to the total which is 15 and remember that have q is going to be happy or Tuesday is going to be double Curtis is a good this week I work for or what we can do two-thirds of the total votes to decide the total being so we know this is Forza 4 is going to be two thirds of State is going to equal 6 equals 6 then we know that she is going to be one third of that Cody is going to or if you remember back we talked about earlier remember from Burrtec destroyed double from centroid to the line so if this is for that means as much as going to finally we have this one if we know that is 3.5 I'm going to try to go the shortcut way on this one JP is 9 then we want to find p a l Magnum PR is going tb130 portion so we're going to double that to get PL which is going to be 7 unit so the entire length of lrl is going to be five years and then we stayed at JP is the 2/3 portion of the line so we have that to get 4.5 4 PS of the entire line JS is going to be 13.5 again do not have to be equal to each other they just have to median and when I meet in the middle that is a centroid okay so let's look at this one if we know that the entire length is 32 then we know that she is going to be today 32in reliable pick the number that didn't really kind of work out evenly but AP then is going to be equal to 64/3 or approximately 21.3 repeating today is going to be one third what the total so it's going to be 30 2/3 or approximately 10.67 repeating if we look here PA remember is Styx is our short portion here the one third portion then that means that CD it's going to be double that so it's 12 Wichita yeah to be 12 + 6 which is 18 do you remember all of these should have their what the last one here we have ep18 so they're bored to get peebee since he p&d alone portion it's a 2/3 portion we're going to getting on units for PB and an eBay is going to equal 18 + 9 at Total Wine so 27 units in as you can see none of these are equal to each other or the actual thickness centroid memory or the actual median equal but they do all meet in the middle of this time terms of solving for a coordinate system of the centroid kind of long way and it will kind of talk about the short way so it's off the Align here like this one in which we had a vertical line at once advantage of a computer horizontal or vertical line so the first thing you're going to do it to take the midpoint of that the middle that's what we're concerned with who's on the midpoint of steamy which would be at the exit 3 + 3/2 Chevy 38 by the way they are pathetic / 2 which would give you 4 but then we take that Nick Point years in my right ear there's a location I'll grab that just to make sure that it did actually beat the big point of that wine then I need to think about what I need to know from two where is going to be 2/3 or from the midpoint 1/3 where is that going to be so I'll find the distance which is going to be square root then get this to work square root I find the distance from a point point that I'm coming from that total lie because I need to know two thirds of the distance not 2/3 in the middle so I do the square root of different than the answers ever different than the wide not even giving so I'm eating to is this entire from a to this point that's too early we could have also kind of counted that just because it was a horizontal line that's kind of the beauty of being horizontal or vertical line if it happens so then we're going to take 2/3 of that number so 2/3 go to is 4/3 and if I notice I'm moving left to right so the only one that I want to do is I need to move my ex by why is not moving at all if you can notice this point being the centroid it's actually going to be why as I'm at 80th and other midpoints which is going to be for now I need to determine if I need to add or subtract I'm starting a 10 and I'm going to go to the right I'm going to add that 4/3 to my app so therefore I will get 7/3 for as my centroid point now we did talk about and I do want you to utilize the fact that we do have a but we do have actually shortcut that we can do here as well so we can go out centroid we're thinking about the center of our entire circle so what we can do here to find the centroid and if I were you this is what I would use every time how to get the background on the other method but really honestly I don't see any point in doing that method. This little short cut in the middle of all three points so we're going to do midpoint of all three points away is 1 + 3 + 3 which are all the exes for the coordinates how to divide that by two I'm going by that I'm sorry about the room I get this to work right right then because there's three points we normally wait about 2 minutes because we're adding two points they were going to add our board plus I-10 but their age I'm worried about that also by 3 because there's 3.2 can I get it all together here for you and what we're going to stay here yes we're going to come up with a centroid that equals 7/3 April 412 / 3 which is made for which is the same thing that I got before I want you to try the next one. I want you to go back actually and try this very next but I have them screen here just kind of give yourself some extra with it you said shortcut method here are Synthroid and just thought I'd be easier to do that so I'm just going to go ahead and add it all kinda in the same step I'm going to head -1 + -2 + 3 + 2 / 3 the entire thing that last three mind you that I'm going to add 5 + 8 + 3 x 10/3 so here the thing so are we getting 0 16 / 3 which is going to be 5.3 relatively so I'm going to go. Just make sure that this does not 0 1 2 3 a 4.3 and that does like right spot on to being the middle of the triangle if I were to connect different points to their through this to their median just spot-on exactly words to where it's supposed to be so make sure you get the work with this make sure you try them on and then do your homework from this section so that why you're really clear on that alright I'll see you guys later

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Section 5.2 (Median)

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