Drawing a reflection
About this video
The instructor reflects quadrilateral ABCD across a vertical line l on a grid. For each vertex he counts how far it is from the line, going perpendicular to it, and places the image the same distance on the other side, producing a mirror image.
You'll be able to
- reflect a point across a vertical line by counting its perpendicular distance to the line.
- draw the image of a polygon under a reflection by reflecting each vertex.
- explain why a reflection produces a mirror image.
Key words
- reflection
- A transformation that flips a figure across a line so it becomes its mirror image.
- line of reflection
- The line a figure is flipped across; each point and its image are the same distance from it.
- image
- The new figure you get after a transformation.
- perpendicular
- Meeting at a right angle.
Transcript
- [Instructor] We're told to plot the image of Quadrilateral ABCD. So that's this thing here ABCD under reflection across line, l. And then we have this little tool here where we can plot what the reflection is actually going to be. So you don't have access to this tool.
This is an exercise on Khan Academy. So if you look for it, you'll find it. But think about what you would do, pause it, and then we can do this together. All right, now let's work on this together. So if I'm gonna do a reflection, and let me move this, all of this out of the way so I can see what's going on a little bit more clearly.
So this is the Quadrilateral ABCD and I'm gonna reflect across this line, this vertical line. So one way to think about it is, we're gonna flip it across this line in a way that essentially it becomes its mirror image. And the way that I'm going to do this is for every point here, I'm gonna think about going perpendicular to this line of reflection and however far I was, I'm gonna go perpendicular on the other side.
So let's say this point corresponds to the reflection of point A. Well, point A is one to the right of this line. So I'm gonna go one to the left and I'm gonna put it right there. Point B, we can see that it is on this row right over there. And let's see, it is 1, 2, 3, 4 to the right of the line of reflection.
So the reflection of it should be 1, 2, 3, 4 to the left. All right. Now point C, it's on that same, I guess you could say row or it's at the same horizontal coordinate, however you want to think about it. But now this one is 1, 2, 3, 4, 5, 6, 7, 8 to the right of it.
So it's reflection is gonna be 1, 2, 3, 4, 5, 6, 7, 8 to the left. So that puts us right over there. And then last but not least, point D right over here, that's one to the right. And it's down here. So I'm gonna go right down here and I'm gonna go one to the left of that same level, and I go right over there.
And there you have it. I have the image of Quadrilateral ABCD under a reflection across line, l. And you could see it looks like it's mirror image. It looks like we're just flipping across onto this side.
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