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Section 9.1 Notes

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This video contains section 9.1 notes that we covered in class (10/3)

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so we can be talking about reflection that we touched on this briefly on Friday when we talked about all three of the different congruence Transformations but today we're going to talk about different types of Reflections you're going to say we're also going to look at some constructions which I'm going to try to walk through and hopefully that keeps well but if nothing else tomorrow we will talk about these reflection construction the game went on transformation and so reflection under a line reflection over a lot of that terminology is really talking about we're fighting something over the line itself sometimes in Iran as well just make sure that you realize they're really saying the same thing so all this is saying is that a point on one side of the line it's image point should be distant from the line so if the point is image should also be one of the other side of the line sometimes the point on the line perpendicular bisector joining the two points I remember we talked about in the last section Section 3 6 how to align is a perpendicular to the line so that's where discount comes in again constructions here so you should have on your desk a protractor to use for these construction I'm a kind of walk you through as well the one thing I never won a year so what you're wanting to do is first want to take your ruler and you want to start at the top here of your line you want your ruler remember we talked about that each point will be a perpendicular to the line between the image point so you want to take you're a protractor and you want to line it up perpendicular to the line not perpendicular to the figure perpendicular to the line L so you going to take your protractor in life perpendicular here then what you want to do do you want to come through slide ruler down I slide your rather down that's fine until you get your first point we should be G when you hit G what you want to do is draw yourself to stay perpendicular line to the line itself through Point G and we want to make sure that we draw that line through Point G perpendicular through Point G live that down and you want to do the same thing bnh you do the same thing through a P&H cuz you're going to have four different lines here through all four of these once you got your lines like this and this one's a little bit thick so that may be why it's not working out so well but once you have your line through all four of the point then what you're going to do me see if I can make this a little thinner Maybe what's you have your mind through all of your points remember that line has to be perpendicular to the red line go through all of those points then what you're going to do is you're going to measure the length from G to the line and you're going to do other side of the line right now she is above the line so they were in a measure that same distance below the line and then put you there then do the same thing with that measure the distance from Earth to the line or longer perpendicular line here and then do that distance from the other side of line L and then repeat that process with E and H 26 lines lined up hairstyle so we should try with the other two I'm still kinda trying to do this one I want you to try with the other two see if you can construct that image the image of it there's one more part I want to discuss about this you know those f and g are going very very close are not on the same line but they are very close to each other so what you got your lines here once you got your lines drawn you got your measurements may know you would measure from YouTube and then go to the other side you're going to put your dad here and we're going to label that g do the same thing with f f goes along this line so the. It's going to be somewhere in here we're guessing I was the only here I have to guess what ruler but we're not going to be guessing you have to measure that actual length and I will be measuring the link to check to see if yours is accurate and age is here so I just going to be about here so then we're going to go live the point here is something very very poor then I want you to remember about the labeling is when we label them we're going to label it not only with the letter but we can't label it exactly the same letter because I know how to use it veggie and then we put a little I'll see if I can put a little Prime like that it's not really a one it's really just a dash but that's called Jeep image of G it's the same as G but it's the image of Southern that would be a prime and then here we would have any Prime and then lastly we would have H prom and sort of you know it look like an exponent kind of is not an x on it but it kind of looks like an x on it in a sentence type in life and we need to do is connect our figure by the last thing that we're going to need to do is connect our figure here so we're just going to take and draw all these lines connect these points together and then we have the image the original figure and you should look exactly like the original My Little off again cuz I didn't have the ruler itself but yours exactly the same as you can take the figure and folded up across a cell and it should look the same on both sides okay so now you say you got two more to do here when I really it was kind of move on to the next step and then at the end of class I want you to go back and practice these two along with the ones in your homework so do want you to do these two one thing I do want to point out on one be here is the fact that Jay actually lives on the line so what that means is Jay prom is also going to lie on the line so for this one is really no need to draw the line through it because your j-prime is just going to be right there it's just going to be exactly like that and then we'll have a problem which is going to be somewhere in here Court you know what she do need your perpendicular line through that and then K Prime is going to be somewhere up in here and then so you connected you'll stay. I need to use a ruler would I do need to be straight I should look like an image of that okay and then you got this one as well know one thing to keep in mind about this one through the figure you're going to notice that he probably is going to end up on the right side where is Q R and S Prime are all going to end up on the left side so if you're lying runs through the figure is going to run through the air as well give me the same thing out of wood step of wood number two year and I want you to look at it but I do I'm kind of skip over now to some of the cauldron problem problems now pulling remind me to go back and do those construction ones talking to him right now but I want you to take the time at the end of class to go back and look at this guy problems now the first thing you need Porta problems you got to grab the figure so you need to go grab the original quadrant where quadrilateral here which is jklm so you see the points here in your direction right here in a graph and connect most points did this one wants you to grab the line Y equals 1 when x equals 1 x equals 1 as we talked about in the last chapter has a Define slope so it is a completely vertical line through one on your ex so the first thing you're going to do every time is graph your original figure then on a coordinate grid we can do like we did before and draw a horizontal line but here's the thing vertical line picture of horizontal line through that but all we have to do when we have a horizontal or vertical line for that matter is we just have to count how many units away from the line so for instance what Jay Jay here is one unit away from the line and it's on the right side so I'm going to go one unit to the left side and put a. And I'm going to label that is J so I'm going to go to minutes away here and that is K Prime how long is one unit away so I go one unit away here that would be M Prime and a nail is one unit away to the right so I go one unit away to the left and then added the last thing you do the first thing you do and got the points label the next thing is we connect all the points together and we got our image at the very last thing you're going to do is we're going to tell what are the coordinates of those points is x equals a number or wipes number to coordinate maybe completely different things in the original so it's not just like oh I went over on my Y axis I'm changing just the way both of these coordinates may be very different so if I look here I look Jay is at 0 3 0 through okay is at -1 - 2 yeah I'm is at 2 211 L is at 0 1 - 1 first you counter space is over label your mind connect the dots and then let's what the coordinates are so I want you to try the next when you're going to try problem number 3 this one you're taking a timing belt drop it again and then they were fighting over the Y equals negative two on that we just talked about ex has a undefined slope at the vertical line so why it was negative two going to be a zero slope and have a big horizontal line you guys don't want you to grab the original garage image label those points and that's what those Point car why you doing that I'm going to also be doing that and I want you to just you do it yourself completely and then what you look up here and check Survivor just like or like you should be able to function of reflection if you are unsure take your paper folded across that reflection line and if it does not match up then you know something wrong if it matches the you're good I thought you should have all of your points draft label and this is the point of gotten Jay was at to -7 K through -6 l - -3 + 0 - -5 all those Aveda Prime now do also keep in mind if you notice how we said me remember I told you that the jkl and am are going to change coordinate but look we reflected over completely horizontal line the x coordinates did not change the only thing that change were reflected over a horizontal line or the y coordinate tiger only moving up and down you look back at the last problem that we did we labeled those you noticed that because it was a vertical line that the only thing that changed where the x coordinate because we were moving boxes we didn't move any up or down we only move left or right where is on this one we moved up and down instead of left or right no. We're going to reflect over the x axis now keep in mind the X horizontal like we had so the last problem cuz the only thing we're going to be moving is up and are what are you going to stay in line with a tape rhymes with the original a which means it going to stay the same X same thing would be C&D they're all going to say perpendicular to that line the coordinates are going to stay the same so go ahead and grab your points off your figure connected always make sure you connect it and then you were going to grab the x-axis and then just like we did before go ahead and start on place Cedar Point go and start plotting your points just like we did before it we're going to see kind of a little shortcut happen with this one you should start saying something that's going to you look so pretty coin coin so a is now going to be at 1 -1 day is going to be at 3 -2 going to be for positive one and day is now going to be at to positive three not only on this one did we keep our previous from your ex's will not change they will always stay the same however your wise change when it's online other than the Xbox go from being a to A- 6 or I can go from so they don't necessarily have any relation on the coordinate that does actually change however when you were fighting over the or under in the y-axis what happens is your ex who sang every time but what happened to your wife take a second with those around you just talk one thing you notice what happened to every single why besides the fact that why change how did it change I hope you say hi hope you know that the relationship is how Chinese did it just went the opposite not a negative or positive it just changed the opposite side one became -1 to become negative to negative one became positive one and positive negative three became positive three so the Sox why when you reflect over the x axis and this is something you got to make sure you know you can always count but you don't answer Evergreen so you need to know this is well for fighting over the x axis the original coordinates of XY go to add negative why was negative I just meaning of opposites that's why I go see eggs opposite why it so that is something again you do want to remember this sit chapter I will be doing the questions at the door and so I will be asking you things like I give you this point to -3 and I reflect you should be able to tell me that it is too positive you know without having to grab that and that sort of thing are you still going to try the next one now this one we use that same figure so you're still again going to rock it but we need to do is reflect over the y-axis vertical line so go ahead and grab these just based on what we've done in the past again the closer that your point is to the line the closer at the image is going to be to the line too far Fairway like things further away the line and ideas so he's going to be farther away than the line today is on your image price on what you two talked about what happens to these coordinates think about the last problem it was a horizontal line and the exit stay the same because we're only moving up and down on the Y and the wise change but are they check where they do the opposite so what do you sort of conjecture what is your conjecture as to what's going to happen for reflecting over the y-axis what do you think's going to happen when reflecting over the y-axis every time not just settling Edie vertical line but specifically that y-axis what do you think is going to happen or what do you notice is happening to the point as you write your coordinates again I hope your notice thing that as your writing is coordinate that the wise guy the same because we didn't change anything otherwise we didn't go up any units are down all we did was we change the exit and because it was specific that specific vertical line the exes changed their opposite the actress Changed by doing their opposite so if it's reflected over the y-axis XY becomes obvious why so biased you just randomly for -1 reflected over the y-axis she should be able to tell me that would be negative because change the x coordinate and then why would stay the same snow the last your bones we have and you only have one on your nose but there's two that I'm going to talk about you are when you take a picture and this is again that same to you figure ABCD lake under or over in the line Y equals X right so go ahead and write your figure grapher line now remember what this line what you what you got to remember yet would be a slope 1 + 8

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Section 9.1 Notes

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