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Determining reflections

A line of reflection is an imaginary line that flips one shape onto another. We find this line by finding the halfway points between matching points on the source and image triangles. All of the halfway points are on the line. Once we find that line, it shows how one triangle reflects onto the other.

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Video 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.