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Identifying type of transformation

Sal is given information about a transformation in terms of a few pairs of points and their corresponding images, and he determines what kind of transformation it can be. Created by Sal Khan.

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  • orange juice squid orange style avatar for user Miguel Henriquez
    I've never been more frustrated in my life, I do not get frustrated easily, as a matter of fact I've never been frustrated, this is the first time I feel angry at math exercises, the quantitatively defining regid transformations is really bad, there is no explanation as to how you can find out where the center of rotation is, there must be a tool that helps you find where you can place the center to do a rotation affecting multiple points.
    (75 votes)
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    • male robot hal style avatar for user KEVIN
      Miguel-
      If you should still be on KA, please know that this particular aspect of Geometry can be tricky to get your head around. I was half-way thru the calculus playlist and exercises and when these Transformations videos and exercises turned up and I found them challenging, to say the least. Others have made this recommendation: start at the top of the playlist and go thru it systematically. Do all the exercises, multiple times if needed, and look at the hints, even if you got something correct. Use graph paper and pencil; get a tactile sense of what is going on. I found some of these exercises cumbersome on the computer screen, but they really pop-out when transferred to paper. If you really feel like you've done everything to understand a problem or concept and you feel that the site is not giving you the right info or confusing info, let KA know. They may take a while to respond but I know that they want to be informed of what is working or not working.
      (26 votes)
  • aqualine ultimate style avatar for user Tayannabanana
    This video makes sense, I get all parts shown is this video and the past two on the subject. However they are nothing like the questions I have been getting in Precisely defining rigid transformations exercise. Also some of those questions don't even have points to the point where i'm not able to figure it out. (I'm talking about the questions formatted with the bubbles, no graphs what so ever). So what do I do about this exercise when I can't even do it.
    (17 votes)
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  • winston baby style avatar for user Ethan Minckler
    what does it mean by
    Preserves angle measures and segment lengths
    Preserves all angle measures only
    Preserves all segment lengths only?
    (7 votes)
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    • female robot grace style avatar for user C C
      Preserves angle measures and segment lengths: means that after whatever transformation you perform, the angles are the same and the lengths of the sides are also unchanged. For instance, if you have a triangle and you translate it by (-7, 3) it is still exactly the same size with the same angles. Ditto for rotations.
      Preserves all angle measures only: means that the lengths may change, but the angles remain the same. For instance, in a dilation, the figure gets bigger or smaller, but the angles don't change.
      (BTW, for those that have done the congruent/similar playlists, the first is describing a figure that is congruent to the original figure after transformation and the second is describing a figure that is no longer congruent but is still similar to the original figure.)
      Preserves all segment lengths only: The angles change but the sides remain the same length. Does anyone have an example for this one?
      (8 votes)
  • leafers ultimate style avatar for user Redstone Werx
    The problem with this video is that it has nothing to do with Precisely Defining Rigid Transformations, which is about whether doing an operation to the coordinates of an object with preserve its angle measures, side lengths, both, or neither. Why is this labeled as "Stuck? Watch a video." when it doesn't help with the subject?
    (8 votes)
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  • primosaur ultimate style avatar for user Radioactive poison
    Please update this video!
    (5 votes)
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  • leaf green style avatar for user KP Kelsey
    Out of curiosity, I wonder where the exercises for this lesson have gone. (At least, I don't see them in this section.) Anyone know?
    (4 votes)
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  • leafers ultimate style avatar for user Prather, Joe
    Is it normal to not be required to watch videos?
    (3 votes)
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    • piceratops ultimate style avatar for user Lincoln Earley
      I'm not 'required' to watch these videos, I just know that he made them for a good reason and I watch them with that in mind. I'm homeschooled so I don't know what your situation is. I also have a bit of OCD so I guess that makes me want to watch all of them so I see a blue checkmark on every .... single ....... video ..... 🤤🤪🥴😵‍💫🫠
      (4 votes)
  • blobby green style avatar for user Attila
    For the problem at : would a rotation around a point like (-6, -6) be a solution? Or any point that all 4 points are equidistant from? (I've just eyeballed point (-6, -6).)
    (4 votes)
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    • marcimus orange style avatar for user Mango
      If you were to rotate from (-6, -6) or (6, 6)... you wouldn't be correct because you'd be moving from blue to purple and green to magenta. Whilst you'd get the same image, which points end up which point is different to what the question needed us to do. We want to go from blue to magenta and green to purple.
      (1 vote)
  • purple pi purple style avatar for user joeboyt
    An associated Exercise says there exists a Map which takes A to A' and B to B'. It also asserts that the quadrilateral AA'BB' is a parallelogram. The hints say thats proof the Map is a translation.

    But what if the translation for A to A' is parallel but opposite in direction to the translation of B to B'?
    Usually in these exercises, we get it wrong if we assume something not given. (E.g., in rotation questions when they say the angle after rotation is the same but they omit that distance is unchanged, the answer is that's not enough info to call it a rotation.)

    What am I missing, please?
    (4 votes)
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  • male robot hal style avatar for user Sun
    At , Sal said that only reflection and rotation works for transformation C. But wait, if Sal translates the first line 9 units to the right and 6 units down, you can see that the first line maps exactly onto the second line! So wouldn't translation work too on transformation C?
    (3 votes)
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Video transcript

Transformation C maps negative 2, 3 to 4, negative 1. So let me do negative 2 comma 3, and it maps that to 4, negative 1. And point negative 5 comma 5, it maps that to 7, negative 3. And so let's think about this a little bit. How could we get from this point to this point, and that point to that point? Now it's tempting to view this that maybe a translation is possible. Because if you imagined a line like that, you could say, hey, let's just shift this whole thing down and then to the right. These two things happen to have the same slope. They both have a slope of negative 2/3, and so this point would map to this point, and that point would map to that point. But that's not what we want. We don't want negative 2, 3 to map to 7, negative 3. We want negative 2, 3 to map to 4, negative 1. So you could get this line over this line, but we won't map the points that we want to map. So this can't be, at least I can't think of a way, that this could actually be a translation. Now let's think about whether our transformation could be a reflection. Well, if we imagine a line that has-- let's see, these both have a slope of negative 3. These both have a slope of negative 2/3. So if you imagined a line that had a slope of positive 3/2 that was equidistant from both-- and I don't know if this is. Let's see, is this equidistant? Is this equidistant from both of them? It's either going to be that line or this line right over-- or that line, actually that line looks better. So that one. And once again, I'm just eyeballing it. So a line that has slope of positive 3/2. So this one looks right in between the two. Or actually it could be someplace in between. But either way, we just have to think about it qualitatively. If you had a line that looked something like that, and if you were to reflect over this line, then this point would map to this point, which is what we want. And this purple point, negative 5 comma 5, would map to that point. It would be reflected over. So it's pretty clear that this could be a reflection. Now rotation actually makes even more sense, or at least in my brain makes a little more sense. If you were to rotate around to this point right over here, this point would map to that point, and that point would map to that point. So a rotation also seems like a possibility for transformation C. Now let's think about transformation D. We are going from 4, negative 1 to 7, negative 3. Actually maybe I'll put that in magenta, as well. To 7, negative 3, just like that. And we want to go from negative 5, 5 to negative 2, 3. So I could definitely imagine a translation right over here. This point went 3 to the right and 2 down. This point went 3 to the right and 2 down. So a translation definitely makes sense. Now let's think about a reflection. So it would be tempting to-- let's see, if I were to get from this point to this point, I could reflect around that, but that won't help this one over here. And to get from that point to that point, I could reflect around that, but once again, that's not going to help that point over there. So a reflection really doesn't seem to do the trick. And what about a rotation? Well to go from this point to this point, we could rotate around this point. We could go there, but that won't help this point right over here. While this is rotating there, this point is going to rotate around like that and it's going to end up someplace out here. So that's not going to help. So it looks like this one can only be a translation.