TenMarks teaches you about transformation on a coordinate plane.
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Learn about Transformations on a Coordinate Plane In this lesson let’s learn about transformations and how we identify them. So, before we start let’s learn about what are transformations. So, transformations are when we take a figure and move them without changing the shape or the size. Shape and size are unchanged. So, ways we can move the figure is we can translate them which means we move them from one place to the other but we don’t turn them and we don’t flip them. We can actually rotate a figure upon an access and that means we turn it or we can flip a figure which means we reflect it. Let’s learn about each one of these three as an example. So, for the first problem wants us to graph the polygon with vertices (1,1),(2,4),(4,3), and (4,1). That’s what I did (1,1),(2,4),(4,3), and (4,1). We took a graph paper and we actually just plot it to four vertices. This is the figure that we get. I’m just coloring it to green. So, once we have this figure, we transform the polygon to new vertices (-4, -2), (-3,-1), (-1, 0), (-1, -2). So, this is the new place for this particular figure. So, we move from here to here. We need to find whether we did our translation, rotation or reflection. So, let’s look at both figures. As we can see each of these points was moved six to the left. So, this point moved five to the left and three to the bottom. So, we move the figure five places left, and three places down. So, we’ve never turn the figure. We never flip it. It looks like this is a translation. In case of a translation, all we do is move everyone of the vertices or everyone of the dots. They equal to the left and the same amount to the bottom. So, in this case if we move five left. This point moved five and three down. So, this is the new point similarly, this one, this pointy moved five and three. Similarly you can see that the other two points. All of them move five spaces to the left and three places down. Since all we did was moved all the points on the figure some places left and some places down. It’s called the translation. Let’s look at different examples. In this scenario as we can see, this is the original figure. Well, in order to get this figure from here to here, what do we do? Well, it looks like I’ve got a line here and all I did was flip it. Now, one way to check so this would be a reflection but let’s double check it. So, we took a point. In case of a reflection, we have this is called a line of reflection. Reflection is like having a mirror here and seeing what the other would look like. So, since we have a line, if it’s in need to reflection then the points would be on the opposite side of the line but the same distance from the top or the bottom. So, this was indeed the line of reflection. Let’s look at point 1. This point is three points away from the line, three spaces. So, if it was reflection, it should come down three spaces which is true. Similarly this one, it’s on the line so it would remain on the line. This one is two points up and came two points down. So, this looks like a reflection. All we did, we didn’t move the figure, we just flip it over our line of reflection. Third one, let’s see what happened. If this is our original figure, how did we get from here to here? What it looks like, all we needed to do was rotate it across this particular point. This is the point of rotation. If we rotated it this way, clockwise you could see the figure landing like this. All of the points would rotate the same angle. So, this transformation is called a rotation. The key thing to remember just to recap is there are three types of transformations that could happen. We could have a translation where we move every one of the points, the same distance, we could have a reflection where each of the points is reflected along a line of reflection like a mirror or we could simply do a rotation where we rotate each one of the points or the entire figure rotates and that’s called a rotation.