In this lesson we will see how to identify transformations. We need to find the type of transformation that’s occurred in each one of the three examples given to us. And the three types of transformations that you need to remember are: there is something called the translation, a rotation, and a reflection. Okay. Let’s learn about each of the figures.
Here, we see in the coordinate plane, we can see that there is a quadrilateral that is shaped like a kite. As we can see it is moved to exactly the same figure, except each one of the points—each one of the vertices, seems to have come down one, two, three units and to the left, five units. So this has gone to a translation of negative five on the X-axis, and negative 3 on the Y-axis. This is called a translation because each point on the graph or each point on the figure has moved X-axis location by negative and the Y-axis location by negative three. It is simply moved or come downwards both Y-axis and to the left, as far as X-axis goes; this is called a translation.
Let’s try the second part. Second part we can see that we have a triangle which see to has been reflected over. The way I know this have been reflected is I can take any of the vertex points; draw it perpendicular -- draw a line perpendicular to the line of reflection, and if this is one, two, three units up, then the reflecting point is three units down, right. It works on all three points, which means this is the line of reflection, so this has been a reflection transformation.
When we look at third example, we have this triangle, okay. As you can see, the point of the triangle—one of the vertices stayed constant and looks like this whole thing has been rotated. How do I know that? Because if I look at this point—the second vertex, the pointy one. It is one, two, three to the left of the Y-axis, and three to the—above the X-axis. Same thing here, has come down one, two, three—and one, two, three, right?
It has been moved over. I rotate this figure, you can imagine that it has come down or actually it has gone rotated this way. It’s been rotated clockwise to get this point over here and this resulting point came here. The length of this and the length of this is exactly the same; so this is a rotation with the center point, the center of rotation being one of the vertices.
Transcription by:
Scribe4you Transcription Services