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### Course: 6th grade (WNCP) > Unit 3

Lesson 6: Transformations- 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

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# Performing translations

Sal shows how to perform a translation on a triangle using our interactive widget!

## Want to join the conversation?

- 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)
- Yes ,first one would look at the x-axis(left or right) and then one would look at the y-axis(up or down).(4 votes)

- How can I write a rule for translation; (x,y)--> ??(3 votes)
- If you shift it a in x direction and b in y direction, it would be (x+a, y+b)(2 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)
- The x-axis is the horizontal line, and the y-axis is the vertical one! Hope this helped!(2 votes)

- so he moves six across to the X-axis it look like he move a bit more and 3 down it looks like 4 or 5(2 votes)
- A translation slides, right?(2 votes)
- how do you translate x^2(2 votes)
- What app or thingy do you use for drawing(2 votes)
- I understand this very well but is there an explanation translations: write the rule?(2 votes)

## Video transcript

- 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.