High school geometry
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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- 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.(70 votes)
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.(21 votes)
- 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.(16 votes)
- Open all of the hints and read them and take notes, then use that information when you go through more questions.(9 votes)
- what does it mean by
Preserves angle measures and segment lengths
Preserves all angle measures only
Preserves all segment lengths only?(8 votes)
- 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)
- 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)
- For the problem at4:25: 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).)(5 votes)
- Not necessarily. You have to remember that you would be rotating along a non-linear line, so it would be somewhat off.
Hope this helps!(1 vote)
- 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?(5 votes)
- It wouldn't be a parallelogram if you translated A in one direction and B in the opposite direction. The line A' to B' would cross the line from A to B, forming two triangles rather than a parallelogram. It helps me to sketch out the situation.(1 vote)
- In1:15, why can't it be a translation? I didn't understand.(3 votes)
- Because one point would have to move 6 to the right and 4 down. While the other would move 12 to the right and 8 down. In a translation, all points should be moved the same distance.(4 votes)
- At2:58, 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?(4 votes)
- 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)
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.