About this video
Triangle ABC is translated by T(8, -1): every point moves 8 to the right and 1 down. Sal moves each vertex in turn, for example B(-4, 8) goes to (4, 7), C at x = -7 goes to x = 1, and A(-1, 2) goes to (7, 1), then connects them to form the image.
You'll be able to
- read translation notation like T(8, -1) as 8 right and 1 down.
- translate each vertex of a triangle by adding to its coordinates.
- build the image of a shape by translating its vertices and joining them.
Key words
- Translation
- Moving every point of a shape the same distance in the same direction.
- Vertex
- A corner point of a shape; vertices is the plural.
- Image
- The new shape you get after the transformation.
- T(a, b)
- Notation for a translation that adds a to every x coordinate and b to every y coordinate.
Transcript
- [Voiceover] Triangle ABC undergoes a translation, and we're using the notation capital T for it, and then we see what the translation has to be. We're gonna move, it's kind of small, I hope you can see it on your video screen. We're gonna move positive eight.
Every point here is gonna move positive eight in the x direction. Its x coordinate is going to increase by eight, or the corresponding point in the image, its x coordinate, is going to increase by eight, and the corresponding point in the image's y coordinate is going to decrease by one, so let's do that.
And I'll focus on the vertices, whoops, let me drag that to the trash, I didn't mean to do that. I'm going to focus on the vertices well, that's just the easiest thing for my brain to worth with. And actually, this is what the tool expects as well. So the point B, is going to move eight to the right, or its corresponding point in the image is going to have an x coordinate eight larger.
So right now, the x coordinate is negative four, if you added eight to that, it would be positive four, and its y coordinate is going to be one lower. Right now, point B's y coordinate is eight, one lower than that is seven. So, in the image, the corresponding point of the image would going to be right over there.
And you see we moved eight to the right, and one down. Let's do that with point C. It's at x equals negative seven, if you move eight to the right, if you increase your x coordinate by eight, you're gonna move to x equals one, and then if you change your y coordinate by negative one, you're gonna move down one, then you're gonna get to that point right over there.
Now, let's do it with point A. So point A's x coordinate is negative one. If you add eight to it, it's going to be positive seven, and its current y coordinate is two. If you take one away from it, you're gonna get to a y coordinate of one. And so there you have it.
Let's see, how do I connect these two? Oh, there you go, and we can check our answer. And we got it right. We have performed the translation.
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