Determine the number of lines of symmetry.Describe the reflection by finding the line of reflection.Where should you park the car minimize the distance you both will have to walk? You need to go to the grocery store and your friend needs to go to the flower shop. Now we all know that the shortest distance between any two points is a straight line, but what would happen if you need to go to two different places?įor example, imagine you and your friend are traveling together in a car. Those relationships may no longer be true after the transformation.And did you know that reflections are used to help us find minimum distances? Relationship to things outside of the things we're transformed that relationship might not. In fact, now it is parallel to the X axis. So this could be C prime D prime is no longer parallel to the Y axis. But after the transformation C prime D prime. So, for example, right over here before transformation, CD is parallel to the Y axis. And you can also look at other properties so how it might relate how different segments might relate to lines that would not be that were not being transformed. Happened to be preserved here is Cs coordinates. After transformation, or their images don't have the same coordinates. So, most of or let me say, coordinates of AB ABD. But D prime definitely does not have the same coordinates as D. C prime, in this case, happens to have the same coordinates as C because C happens to sit on our, the line that we're reflecting over. B prime has different coordinates than B. So as we see, the image of A A prime has different coordinates than A. And this just goes back to the example we just looked at. Well, what is not preserved? Not preserved. Lengths and the same angles, the perimeter and area are also going to be preserved. Side lengths, the distance between A and B is going to be the sameĪs the distance between A prime and B prime. So, for example, this angle here, the angle A, is gonna be the same as the angle A prime over here. Preserves the lengths between corresponding points. That's actually one way that we even use to define what a So what's preserved? And in general, this is good to know for any rigid transformation The reflection looks something like this. The real appreciation here is think about, well, what happens with I really just want you to see what the reflection looks like. Know for the sake of this video, exactly how Iĭid that fairly quickly. And so our new when we reflect over the line L. And since C is right on the line now its image, C prime, won't change. But you don't have to know that for the sake of this video. So what it essentiallyĭoes to the coordinates is it swaps the X and Y coordinates. And we can even think about this without even doing the What is preserved, or not preserved as we do a reflection across the line L. In this situation let us do a reflection. Let's do another example with a non-circular shape. To here we went to the coordinate we went to the coordinate So for example, theĬoordinate of the center here is for sure, going to change. But, they'll preserve things like angles. We don't have clearĪngles in this picture. We're transforming a shape they'll preserve things And this is in general true of rigid transformations is that they will preserve the distance between corresponding points if And you could also thatįeels intuitively right. They're gonna have all of these in common. Radius is preserved and then the area is also going to be preserved. In fact, that follows from the fact that the length of the radius is preserved. Well, if the radius is preserved the perimeter of a circle which we call a circumference well, that's just aįunction of the radius. The radius here is also is also two, right over there. Things that are preserved well, you have things like the radius of the circle. Under a rigid transformation like this rotation right over here. That are preserved or maybe it's not so clear, we're gonna hope we make them clear right now. So you got to forgive that it's not that well So our new circle, the image after the rotation might And let's say our centerĮnds up right over here. So let's say we end up right over so we're gonna rotate that way. Of argument we rotate it clockwise a certain angle. We take this circle A, it's centered at Point A. Rigid transformations which means that the lengthīetween corresponding points do not change. Think about rotations and reflections in this video. Of a shape are preserved or not preserved, as they undergo a transformation. Going to do in this video is think about what properties
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