About this video
Sal finds the line of reflection that maps triangle ABC onto A'B'C'. C and C' are six units apart, so he places a horizontal line halfway, three units from each, and checks it with A (5 units each side) and B (6 units each side). The line is y = 1.
You'll be able to
- find a line of reflection by going halfway between a point and its image.
- check a line of reflection using every pair of corresponding points.
- explain why a point and its image are the same distance from the line of reflection.
Key words
- line of reflection
- The line a shape is flipped over; each point and its image are the same distance from it.
- horizontal line
- A flat, left-to-right line, like y = 1.
- corresponding points
- A point and its image after a transformation, like C and C'.
Transcript
- [Instructor] We're asked to draw the line of reflection that reflects triangle ABC, so that's this blue triangle, onto triangle A prime B prime C prime, which is this red triangle right over here. And they give us a little line drawing tool in order to draw the line of reflection.
So the way I'm gonna think about it is well, when I just eyeball it, it looks like I'm just flipped over some type of a horizontal line here. But let's see if we can actually construct a horizontal line where it does actually look like the line of reflection. So let's see, C and C prime, how far apart are they from each other?
So if we go one, two, three, four, five, six down. So they are six apart. So let's see if we just put this three above C prime and three below C, let's see if this horizontal line works as a line of reflection. So C, or C prime is definitely the reflection of C across this line.
C is exactly three units above it, and C prime is exactly three units below it. Let's see if it works for A and A prime. A is one, two, three, four, five units above it. A prime is one, two, three, four, five units below it. So that's looking good. Now let's just check out B.
So B, we can see it's at the y-coordinate here is seven. This line right over here is y is equal to one. And so what we would have here is, let's see, this looks like it's six units above this line, and B prime is six units below the line. So this indeed works.
We've just constructed the line of reflection that reflects the blue triangle, triangle ABC, onto triangle A prime B prime C prime.
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