About this video
The video reflects quadrilateral JKLM over the line y = x. It shows that this reflection just swaps the x- and y-coordinates, written (x, y) -> (y, x), and applies the swap to each vertex to graph the image.
You'll be able to
- describe a reflection over y = x in coordinate notation as (x, y) -> (y, x).
- find the image of a point or polygon after reflecting over y = x.
Key words
- reflection
- A transformation that flips a figure over a line, like a mirror image.
- line of reflection
- The mirror line a figure is flipped over; here it is y = x.
- image
- The new figure after a transformation; its points are labelled with primes, like K'.
Transcript
- [Instructor] We're told to graph the image of quadrilateral JKLM, after a reflection over the line y equals x. And then later, we wanna describe the reflection in coordinate notation. So pause this video, give this a try, and then we'll do this together. Okay, now let's work on this together.
So we wanna reflect over the line y equals x. So let me just draw that out a little bit, so y equals x looks like this. Make sure it's hand drawn, so it's obviously not perfect, but this gives you a sense of the line y is equal to x. And you might already know the transformation here.
To transform over that line, what you wanna do is take your x and y, and you essentially just wanna swap them. So what was the x will now become the y, and what was the y will now become the x. And that's essentially all you need to do. So we actually know the second part right over here, this is just going to be a y right over here, and this is going to be an x.
But let's actually graph this image. And so what we wanna do is we could look at each of these points. So, for example, point K, right over here is at the coordinate -1, -3. So if we were to swap these, you'd get to -3, -1. So this right over here, we could call that K prime, and actually, let me do all of these in a different color.
So if we look at J right over here, J is at -1, and then this looks like -5, 6, -6. If you were to swap that, you would go to -6 and then -1. So, let's call that J prime after you've mapped it. And now, let pick another color here. So point L is at the point five, -3.
So if you were to swap those, you go to -3, five, you're going to go right over here. So this is L prime. And then last but not least, let me see what color have I not used? I will use this teal color. So point M right over here is at the coordinates two, -6. So if you were to swap the two and the -6, you go to -6, two, which is right over here.
This is where M prime would be, and so we now see our new quadrilateral, if we just connect these points. We have now mapped it, and I'm doing this by hand. This is a screenshot of the Khan Academy exercise. Over there, you actually have a tool, where you can move around the points in order to do the transformation, but it's gonna be the same idea.
You look at each of these coordinates, and then you're gonna swap the x and the y for a reflection over the line, y is equal to x, and we're done.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.