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Coordinate Problems Review Worksheet Video

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This video contains the work and solutions for the coordinate problem I gave you on Thursday. I would would make sure you listen about when to pause the video so you do not get the answer before you do the work!!

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as I want to go through with this with you I'm about to be in class today so that way if you do have any questions and also I need to know if you need to watch the video that's perfect make sure you're ready for your quiz tomorrow member the quiz is on Friday so the first question you ask you to verify or classify the triangle by its angles and sides so first you want to sort of crap here here is what we got it we say that 808 obviously is really hard to tell this angle I hear you know it obviously being that you're definitely a cute but I tell if it's maybe if it's right or acute so what you want to do angles we would want to check to see if I claim I possibly are right angle of slope formula tried to the slope formula here is going to be the difference in the y s o y sub 2-1 by someone / X sub 2 - x someone so you're going to the slope of line AC and the slope of line a v if they do turn how to be perpendicular to each other that makes an angle a perpendicular or the right angle guy so I want you to try that before in just a minute before moving on in the video I do and I'll tell you when the kind of pause it but I want you to Prodigy doesn't try to call then and I don't want to hear what comes out to be not a classified by sides we need to know the length of each side so we're going to do the distance formula are the plot are the side so that's going to be the square root of X2 - X1 Plus why I 2 minus y1 and I remember all of that is under a square root so you're going to find the length of a b baby the length of the base and the length of anything to determine if the triangle is isosceles scalene or equal equilateral if and if all three of the same it's going to be Skyline now at this point what I want you to do is pause the video and do those two things do the slope do the distance before moving on anywhere in the video because next I'm going to show you if you are got it that's fine keep going because I want to show you the results of this and I don't want you to really look at it until you practice it cuz that's really kind of the best part here okay so if I do need a distance of 8 I did radical 20 which is 2 radical 5 BC is too radical 10 and AC is too radical $0.05 80 + AC or equal to each other that made the triangle is isosceles as you can see the slow but I see is negative to the song she is one half so therefore that Linda's to know that the perpendicular are perpendicular to each other so it's a right triangle has a right angle angle a so it is an isosceles right triangle now this is really going to help us in a right triangle is really going to help us when we start looking at where these points of like circumcenter and orthocenter where they should meet at right so now it's on to doing a circumcenter okay so a circle is the point at which three perpendicular bisectors mate for the first thing you want to do is create yourself a charger now the quiz tomorrow I will have the chart for you so that you can kind of you know Phil Landon and organize your stuff but it did will know be labeled I guess you have to know what goes on there so it's a perpendicular bisector we need to write an equation of a perpendicular line to each of these three line so I need to know the slope of the line then I'm going to use the perpendicular slope esperar equation then it since it's a bisector perpendicular bisector what that means is that I've got to find the midpoint of each of these life is over to find the midpoint of a baby cuz that's the point going through and we're going to use the perpendicular slope to write the equation now remember the equations in this box right here that is going to be the perpendicular bisector equation it's not the equations equations of each part regular bisector so the big ten things you need to know about solving for the perpendicular bisector equation for slope so slope of the line opposite reciprocal then find the midpoint of the two points of the midpoint of AD or the midpoint of BC or AC River midpoint formula just so you remember since the guards of a distance to the flow point formula is where we take an add the exit so we do X1 plus X2 can we divide that by two hoping then we take y 1 + Y 2 and we divide that whole thing about you so again play keep going on the video but right now I really need you to try this on your own do not go past the video until you tried it on your own because you're not going to be able to do it on the quiz tomorrow if you don't do that remember make your turnout was slow the right now go find the slope of a b think about what would be the perpendicular slope of a b then find the midpoint of a baby then you're going to lose the perpendicular slow and the midpoint to write the equation each perpendicular bisector once you've done that for each of these through what you find slope equation for each line then you need to grab it again. love you too but graph each of the one right now okay so after you find the equation each one go ahead and grab all three so we can see where they should land I remember from the previous problem is a right triangle which hey Don are graph we should see all three lines meeting on the triangle like it literally is going to meet somewhere on the triangle like on the sides of either a c a b or B C it's literally going to touch that the other thing we would want to do is we want to grab don't diminish the graphing right always grab to see to check two things one that it does meet on the triangle in this case or outside if it's up to sore inside if it's a cute second the thing that you're looking for is that it is going to need it exactly the point that you're going to find so after you get all three equations written you're going to take two of the three it does not matter which two you take that's the key matter which two you take take two of the three equations and you're going to set them equal to solve for x and then plug back in to solve for y and I will give you your point of the circle the actual order pairpoint you put cities around it, between the littoral ordered pair so I'm going to the next screen now and talk about the anchors but if you have not solve this equation please do it right now stop the video pause don't go forward until you I'm have audit all done grabbing everything so it's done tired thing so that way you can check your not right that's okay but I want you to be able to check and I just followed exactly what I did so as you can see here you see that on the slope of a b is 1/2 so perpendicular slope is negative to the midpoint is 4 so the equation is y equals negative 2x + 8 + I go grab that right I go k+ down -2 and I grab that why do you see the slope is negative 1/3 perpendiculars 3 2.3 has or 32322 y equals 3x - 7 I didn't show how to solve for this but I think at this point you should be able to take this club in that point and thought for this equation you know if not you need to email me ask me questions something alright see the slope is negative chuso perpendicular one half the midpoints one once a y equals 1/2 x + 1/2 so after you get them all the equations and you grab them we see that they do need right here but sometimes that's not a perfect just ordered pairs we need to make sure that we always do it algebraically well as graphically so I'm going to take two to three questions I chose to pick the blue and the red equations and I'm going to compare them that I've got to X can you text my baby eagles 3x - 7 so give me x equals 3 as you can see here and then I take that back and plug it in over here to get y equals 2 so the circumcenter point is that .32 a point positive three positive check so it also one thing I said make sure that you brought it as well as dude algebraically because you're checking two things when we look at .32 right here that it is on the traffic literally on side BC which is expected by the right triangle here also it shakes out that if I go to look at my grass that is .32 which is what I said algebraically that it should be thanks for looking for the centroid now on your sheet it does say mid Center that's another word for centroid but it but it is worth looking for the centroid here now remember the centroid is that the midpoint it's it's where the three medians right so we have that shortcut dad said that we can add all the X's up and divide then all the wide and divided by 3 and of course that is to add all of those things okay now what other thing you might just want to check is that a graphically work so why would you have a problem please do it right now before you move on pause the video right now until you've done it and then we'll go on and check so what we see is that if we add all the EX's 4 + 3 + 1 + 8/3 and then why they are plus 2 plus 1 gives us 3 or 3 which is one of the centroid is 8 third one or approximately 2.671 so it's going to be right in here remember I sent you should always be inside the circle so different than a circumcenter cosigner the centroid should always be in the center of the circle which is why we are not circle of the triangle is always being the center of the try all right now one thing I did hear just a check to make sure these are right as I found the midpoint baby and I connected Point see which is a vertex to the midpoint I did the same thing with BC I found the midpoint and connected to that point and I did finally I did the same thing with a c I found the midpoint of AC and connected be the vertex so they three colored mine or my median and I just wanted to do that to check on my grass that they did actually all three go through this point 2.671 or 8/3 one that I thought I would finally we're going to talk about the orthocenter now here's a good thing about the orthocenter to work smarter not harder God the orthocenter is the altitude is where three altitudes will altitude mean they go from the vertex what you're already going to be given here right if ad is the line that means thing should be your vortex if they see is the one that means I should be your protective case is online that means point B should be a vertex cool right here is pretty easy to fill out you got all the things you have to do no work you just have to know which one goes where all right now the other two columns since the altitude goes from the vertex not the midpoint so it should discharge should not look exact we like your chart from circumcenter but there are some commonalities because the perpendicular bisector is perpendicular to the line at touches and an orthocenter is perpendicular to the line that touches then the two columns is first to call the slope and the perpendicular bisector or perpendicular slope both of those two columns should literally look verbatim they should look exactly the same so for instance if this one does 1/2 and this one is negative two I don't have to do those again right I see that that's what they already are if the slope of BC was -1/3 and it's here is three I don't have to do anything I just go back to my other short and literally just copy of verbatim here we got negative 2 and 1/2 so so far I've done no work for this problem I've gone to my purple guy gone to my apartment Factor equations by circumcenter chart and I literally just copied these three exactly down I copied this column exactly down I went and saw since Abby was my line see was my vertex BC so I was my birthday Stacey so be with the only work I'm really going to have to do in this chart is to write the equation now remember you're going to be taking the perpendicular slope column and the vertex call to write the equation now because work get our bisectors use midpoint and not the vertex that means it's called will be different they will not be the same numbers at all this equation is well will be different the equation called. Going to be different so before you move on do you have any during the next flower in the next little bit I want you to pause the video over in just a minute because I want you to write the equations I want you to graph the picture and then I want you to solve by substitution to find your orthocenter okay sounds positive you don't have you have not done this question hey so now let's look what we got we already said the slope 1/2 -2 and a virgin 03 one-third 3-day take days to 1 beta 2 1/2 vertex B is 61 so by equation came out to be why it was negative 2x plus 3y equals negative or positive 3x - 7 + y equals 1/2 x -2 again if you're not getting these equations but you got all of this email me let me know why you're not getting it because this is solving an equation the most important thing about all this is you have to make sure that you're kind of double-checking your cell on the way cuz if even one of these is wrong if the fuse number check the fuse wrong slope if you forget to do the opposite reciprocal of a slope to be perpendicular equations going to be wrong if the equation in your grass and your solving is going to be wrong the whole answer is wrong so you have to make sure that you go through and consistently are making sure you're doing it correctly I'm on the way so now I grabbed all three lines and I see that they met here I compare two of them -2X what's 3 + 3 x - 7 to get access to play back in I get Wyatt -1 something about orthocenter pointed that to -1 again just like with circumcenters if it's an obtuse angle it should meet out if it's an acute angle I should meet you inside if it's a right triangle which is okay if it is a right triangle is to meet on and you say it literally Meats in this case on point eight and what you can see in the circumcenter was 3 to the centroid with a third one the orthocenter was to -1/3 not the same number don't don't feel like they have to be the same number I don't even know how to play know if it's and it's an area there might even be the same number maybe an equilateral triangle possibly but otherwise really not like you're not looking for them to be the same number so just be really careful there so the orthocenter Point here is that two negative one again we want to bar graph that it makes on which it does and we want to check that this point to negative one is where they actually were meeting both graphically here and algebraically here and we see that they are so why a couple thoughts on this is that make sure a couple of things first of all make sure that you know that perpendicular bisectors you need to find the slope perpendicular slope midpoint and write the equation graph compare them by substitution and then make sure your graph an algebra algebraic work is the same perpendicular bisectors remember can meet inside outside or on the triangle for centroid make sure that you take and divide Battle of the exes / 3 / wise / 3 you're fighting the center of the triangle do remember a centroid will only ever be in the center of the triangle not outside not I'm on the train alright by the way the orthocenter you're going to use slope and perpendicular slope literally copy this verbatim from your other one do not have to do this again unless you just want to check cuz you think for some reason you're not correct it's the vortec Tangled not the man which major equations are going to be different you're going to grab those equation solve them using substitution and then check that your algebraic answer does match your graphical answer also finally on same thing as the circumcenter the fact that if you have if you have an obtuse triangle it outside acute inside right like a new case it's on the train so I'm not going to be there tutoring tomorrow and I'm not going to be there for class so you need to make sure that I'm if you are having any questions that you email me by like Thursday night I probably won't be answering emails pretty much on Friday so please please make sure that you email me before you you know we're doing any of this alright I will see you guys when

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Coordinate Problems Review Worksheet Video

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