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### Course: 6th grade (WNCP) > Unit 3

Lesson 6: Transformations- Intro to reflective symmetry
- Rigid transformations intro
- Performing translations
- Translate points
- Rotating points
- Rotate points
- Performing reflections
- Reflect points
- Finding a quadrilateral from its symmetries
- Finding a quadrilateral from its symmetries (example 2)
- Reflective symmetry of 2D shapes

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# Performing reflections

Sal shows how to perform a reflection on a quadrilateral using our interactive widget!

## Want to join the conversation?

- At0:26, Sal moves the reflecting tool line to the line y=x+2. How does he know to move it at that point? How does he know where y=x+2 is?(5 votes)
- He knew that by using two pieces of information:

1- the slope of the line/reflecting tool which is the coefficient of variable x.

2- the y-intercept which is the intersection of the line/the tool with y-axis. The value of y-intercept is aways the constant in the right-hand side of the equation.

Hope this helps!(7 votes)

- Concept of reflection, that I can understand. Coefficient of x=1? Slope of 1? There you completely lost me. This reminds me of why I didn't understand math in high school 30 years ago. These sound like algebraic concepts, and I started with lower lessons because I wanted to work my way up to algebra, which is where my learning really went off the rails years ago. None of these "simple" explanations in the comments are doing it for me. A link to the lesson that explains these concepts, for reference, might help immensely. Otherwise, I'm almost at the end of the line with KA. Trying to explain a new concept with a concept that hasn't yet been taught makes exactly zero sense. In the form of an equation, makes sense=0. Please explain, or link to an explanation, that uses terms someone who hasn't learned algebra yet can understand. Thanks.(5 votes)
- I'm afraid that the Geometry course actually assumes you've already gone through both Algebra I and Pre-Algebra - if you click on 'subjects' over at the top left of your screen, you'll be able to see that they're formatted in that order. If you watch videos out of order, it's only to be expected that some concepts you haven't learned yet will show up.

However, some links you might find useful: the Algebra 1 course is at https://www.khanacademy.org/math/algebra, and the specific lessons that teach you about slope are here https://www.khanacademy.org/math/algebra/two-var-linear-equations#slope. ('Coefficient' is basic algebra vocabulary, and an explanation can be found in the very first algebra lessons.)

I hope this helped you; hopefully your experience with KA is improved by this tips. Wishing you good luck from a fellow KA student - although I'm still in school, instead of 30 years out :)(5 votes)

- I did not quite understand how SAL found the points 'y=x+2'... How do you do that?(3 votes)
- Consider the equation, y=x. The value of y is always the same as x. When x is 3, y is 3. When x is -105, y is -105. When x is the square root of pi, y is the square root of pi, etc. When graphed, a diagonal line is drawn through the origin (where x=0,y=0) and one end goes in the upright direction,

and the other end goes in the downleft direction. Saying that y=x+2 means that y is always 2 units more than x, therefore moving the line up 2 units. When in doubt, just plug in any number for x and use it to find y.(4 votes)

- but how do you do it without the tool, please make a video about that please like so it can go to the top and Khan can see this(4 votes)
- i dont understand how to do the y=x+2(4 votes)
- you plug in numbers for that equation.

if x=0, then y= 0+2, and therefore y=2 when x=0.

if x=1 then y=1+2, and therefore y=3 when x=1.

when x=2 then y=2+2 and then y=4.

plug it in, plug it in.(1 vote)

- I can't manage a reflection after I establish the reflection line. Can't manage the widget! Any Ideas to help me?(5 votes)
- no, uhh, thee's this weird symbol line in the middle of the line, just click the half of it which isn't orange.(0 votes)

- I think that the more mistakes that you make, the more you learn; because you learn from your mistakes, and then build on them to answer correctly.

You know what you did wrong, and you won't repeat it. If you never made mistakes, you would never know how to react to them. You then learn from them great things that enable you to build around them, to a higher place that has never showed its face to you. As you soar to higher lands, you will make mistakes in the process. But, don't beat yourself up! For the very thing that you may feel bad about, may be the thing that led you to the higher place where you are today.🏆🥇📕(2 votes)- so say the "y-intercept" is 2, you would find the number 2 on the y-axis and then from there you would go up one and over to the right one. until you have enough points then you start to go down one over one to complete your line. If the slope is -1 then you would start by going down 1 and then over to the left one.(3 votes)

- what is the site they use(2 votes)
- in1:02what does he mean by "when x is equal to zero y is equal to 2"does he mean that every time you go one to the right , you go 2 to the y direction?(1 vote)
- No. He's talking about the y-intercept (the point where the line intercepts the y axis). Points on the y axis have an x value of 0. So if y is 2, x will be 0.(3 votes)

- What if I do a problem similar to the one that Sal did in the video but instead of y=x+2 what if the x is a 9 or -9?(1 vote)

## Video transcript

- We're asked to use the
reflect tool to find the image of quadrilateral PQRS, that's this quadrilateral right over here, for a reflection over the line y is equal to x plus two. All right, so let's use the reflect tool. So let me scroll down. So let me click on Reflect, it brings up this tool, and I want to reflect across the line y is equal to x plus two. So let me move this so it is the line y equals x plus two and to think about it, let's see, it's going to have a slope of one, the coefficient on the x term is one, so it's going to have a slope of one, so let me see if I can give this a slope of one. Is this a slope of one? Let me put it a little bit -- yep, it looks like a slope of one as the line moves one to the right. We go from one point of the line to the other, you have
to go one to the right, and one up or two to the right, and two up, however much you move to the right in the x direction, you have to move that same amount in the vertical direction. So now it has a slope of one, and the y intercept is going to be the point x equals zero, y equals two, we see that right over here. When x is equal to zero, y is going to be equal to two, so let me move this. So we see that we now
go through that point. When x is equal to zero, y is equal to two. And now, we just need to reflect PQRS, this quadrilateral, over this line, so let's do that. There you go, we did it. The things, the point, like
point S right over here that was to the top and left of the line, its reflection, the corresponding point in the image is now to
the right and the bottom of the line. The things that were to the right and the bottom of our line, like point P, it's the corresponding
point in the reflection is now on the other side of the line. So there you go, I think we're done, and we got it right.