Determining a reflection
About this video
The instructor works out which of three rectangles is the reflection of figure K across a diagonal line L. He reflects one vertex by going perpendicular to the line and the same distance beyond it, which already identifies rectangle C, then checks the other vertices by counting diagonal squares on each side.
You'll be able to
- reflect a point across a line by going perpendicular to it and the same distance on the other side.
- reflect points across a diagonal line on a grid by counting diagonal squares.
- identify which figure is the reflection of a given figure.
Key words
- reflection
- A flip of a figure across a line that makes a mirror image.
- line of reflection
- The mirror line; each point and its image are equally far from it on opposite sides.
- perpendicular
- At a right angle to a line.
- vertex
- A corner point of a shape.
Transcript
- [Instructor] We're told, select the reflection of figure K across line L. So this is figure K, and we really need to figure out which of these is its reflection. So pause this video, have a go at that before we do this together. Okay, so a reflection, I think of it as a mirror image across this line, L.
It's almost like if this were in the sky and this were the surface of the water, it's kind of hard to orient you that, maybe we're at the bottom of a planet or something. Or if you put a mirror here, what would its reflection actually look like? And the way that we can think about this is we could take each point and think about where would its reflection be.
And the way to do that is you can take a perpendicular from the line of reflection to that point. So for example, that right over there is perpendicular to the line of reflection. And we can see if we go that same direction on the other side of the line of reflection, but still perpendicular, that's where the corresponding point of its reflection should be.
So if we go over here, that should correspond to this point right over there. And actually, that's already enough to answer the question. If we know that the choice is between A, B, or C, the only of these three figures that contains this point as a vertex is point C, or is rectangle C.
So I could either, I can already tell you that the answer is going to be C. But just to validate that, let's look at the other points here. So if I were to take, I'll do it in different colors here so we don't lose track. So this vertex right over here, that corner.
So if I were to drop a perpendicular to the line of reflection and then go in that same direction, if I am essentially going diagonally through two units right over here, I get to this point right over there. And I can keep going, I can do it with this one over here.
If I have a perpendicular, I'm essentially going diagonally through three of these squares. If I go diagonally through three of these squares again, yes, I get to that point right over there. And you would see the same thing as if you looked at this one over here.
You're diagonally going through, let's see, four of these. So if you go on the other side and you diagonally go through one, two, three, four, yes, we go right over there. So we can feel very good that choice C is indeed the reflection of figure K across line L.
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