6th grade (WNCP)
- Intro to reflective symmetry
- Rigid transformations intro
- Performing translations
- Translate points
- Rotating points
- Rotate points
- Performing reflections
- Reflect points
- Finding a quadrilateral from its symmetries
- Finding a quadrilateral from its symmetries (example 2)
- Reflective symmetry of 2D shapes
Sal shows how to perform a translation on a triangle using our interactive widget!
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- When Sal says X or Y direction, he means along the X and Y axis right?(16 votes)
- Yes, because he is showing how to do translations. So to translate, you have to move the object on the x and y axis.(5 votes)
- so the first number is a left or right and then the second is up or down?(4 votes)
- How can I write a rule for translation; (x,y)--> ??(3 votes)
- Why is it called a rigid transformation and what makes it so unique? Thanks.(2 votes)
- It's called rigid because we're not twisting or doing anything else weird to the figure.
You'll learn later that these transformations can be expressed as matrices, rectangular arrays of numbers. What makes these types of transformations unique is that
1. All of them can be expressed as matrices
2. All transformations that can be expressed as matrices are just combinations of these transformations
So these transformations serve as a helpful way to visualize what matrices are, since they mirror them so closely.(2 votes)
- which one is the x and which one is the y(2 votes)
- Let's do an example on the performing translations exercise. Use the translate tool to find the image of triangle W I N for a translation of six units, positive six units, in the X direction and negative three units in the Y direction. Alright, so we wanna go positive six units in the X direction and negative three units in the Y direction, alright. So, I click on the translate tool. Click on the translate tool and I wanna go, so, I wanna go positive six units in the X direction. So, I can pick any point and go six to the right and everything else is gonna come with it. So, one, two, three, four, five, six. So, I did that part, I translated positive six units in the X direction and negative three units in the Y direction, so everything needs to go down by three. One, two, three and notice, I focused on point N and this is it's image now, or the image of point N, this whole triangle is the image of this entire triangle, the triangle W I N after the transformation, but you see that every point shifted six to the right, six to the right and three down. This point over here, six to the right would take you, let's see, it's at one and a half right now. It's X coordinate is one and a half. It's new X coordinate is seven and a half, so it's X coordinate increased by six and it's old Y coordinate, or the original Y coordinate was six and now, in the image, the corresponding Y coordinate is three. So, it has, we have shifted it down three. So, we see that that's happened to every point here and we're done.