TenMarks teaches you how combinations of transformations.
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Learn about Combining Transformations In this lesson let’s learn how to combine transformations. We’ll do a few very interesting problems. We have to find what combinations or transformations are shown below. Problem A, one represents what the original figure was. Two is the next step and three is the final step so let’s look at them. So, the figure was a triangle which was in place one. What transformation do we do to get it to figure two? Well, as we can see, it looks like the triangle was flipped over this particular line so transformation one to two was a reflection. All we did was basically flip this over in this line. So, this is a mirror image of this. So, now to get from two to three, what do we do? Well, it looks like this point moved over here, this point moved over here and this point stayed where it is. So looks like it was rotated by 90 degrees because all we did was have this which was have this which was laying flat to stand up straight. In this particular line instead of laying flat landed up straight. So, the angle of rotation is 90 degrees. So, again what we did was first we’ve reflected figure one to get to figure two and then we rotated the figure to get to figure three. Let’s try couple more. In this scenario, this is figure one, this is figure two. What do we do? Well, if to get from figure one to figure two. This is going to be a trick you want. Well, it looks like the figure was flipped over but it’s not really flipped over because if it was, it would be a mirror image here. It’s actually being rotated by 180 degrees. What we’ve done is across this line or this point of rotation. We’ve rotated this figure at 180 degrees. All the way until it reaches this particular point so we’ve rotated it at 180 degrees. Imagine if you rotated this figure and we just turned it, all we did was turn this figure and this part would arrive at the bottom, this part will arrive at the top. So, the first thing we did is rotate it from one to two and get figure one rotated by 180 degrees to get to figure two. Once we have figure two. The shape of two and shape of three is exactly aligned except, it is one space up and four spaces to the right. So from point figure two, to figure three we translated it. How much do we go? One up and how much did we go right? Four to the right so, we translated one step up and four places or four steps to the right. As you can see each one of these points to this corner went one up, one, two, three, four to get to this point. I’m using different color. In this particular point we went one up, one, two, three, four to the right. In this point went one up, one two, three, four to the right. All the points moved exactly one point or one square up and four squares to the right. Let’s try the third problem. The third problem, we have figure one. Figure one got to figure two. Well, this was obviously to get from figure one to figure two. They’re exactly the same. We did our translation. How much did we translate? Well, in this particular point went six points down and then five to the right. So, six down, five right. Let’s double check that, let’s take another point of this one. Six down, five, that’s where it ended up so this is correct. Now, to get from figure two to figure three what transformation did we make? Well, if you look at this, the figures have been flipped over. So, we know it’s a reflection, but the line of reflection is right here. So every point, if this point was two steps down, at this point was two steps down. Now, it is two steps up. This point was two down, it’s two up. This one was four down, and it’s four up. You got the idea. So, essentially what we’re learning is to move from one place to the next place. We could actually transform it and do combinations of transformations whether to rotate first then translate, reflect first then rotate but similar figures can land up in different places by rotation, reflection and translation.