Video Transcript
Reflect triangle B in the 𝑦-axis and then in the 𝑥-axis. Which triangle is its image?
We begin by recalling that when we reflect a shape in a mirror line, we flip it. We want to reflect shape B, that’s this one, in the 𝑦-axis, that’s this vertical line here. And so we know that we’re going to flip the shape B about this line. And its image will be the exact same distance from the line on the other side. We could do this vertex by vertex.
Let’s start with this vertex here. Its perpendicular distance from the mirror line is two units. And so the perpendicular distance of its image must also be two units but out the other side. And that gives us this vertex here. So we’re safe to assume that the image of B after the first reflection is triangle D. But let’s just double check.
Let’s have a look at this vertex. Its perpendicular distance from the mirror line is three units. And in fact, we see that the corresponding vertex on D is the same distance away from the mirror line on the other side. So D is the image of B after its first reflection. But then we’re told to reflect this in the 𝑥-axis. And so now we’re going to be reflecting in the horizontal line shown.
Now, it might be quite obvious to you which triangle we’re going to look at. But let’s do this vertex by vertex once again. The first vertex we’re going to choose on triangle D has a perpendicular distance of two units away from the mirror line. Two units away from the mirror line on the other side brings us to this vertex on C. And in fact, we could do the same thing with the other two vertices on our triangle. Either way, we see that the image of D after the given reflection is triangle C. And so if we reflect triangle B in the 𝑦-axis and then in the 𝑥-axis, triangle C is its image.
But in fact there was another way we could’ve answered this question. We know that if we reflect a shape in one axis, and it doesn’t matter which, as long as we then follow it by a reflection in the other axis, that’s the same as a rotation of 180 degrees about the origin. We can in fact see that B can map immediately onto C by this very same rotation. Either method is completely fine as long as we notice that the image is C.
