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Determining reflections

Finding the line of reflection by considering the image and the source of the reflection.

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  • blobby green style avatar for user ramona.spencer
    are there any tricks or rules with rigid transformations?
    (20 votes)
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  • blobby green style avatar for user Barilugbene261
    How do change figure across the y-axis
    (6 votes)
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    • duskpin ultimate style avatar for user Polina Vitić
      To "reflect" a figure across the y-axis, you want to do two things. For each of the figure's points:
      - multiply the x-value by -1
      - keep the y-value the same

      For instance, Triangle ABC (in the video) has the following three points:
      A (2, 6)
      B (5, 7)
      C (4, 4)

      To reflect Triangle ABC across the y-axis, we need to take the negative of the x-value but leave the y-value alone, like this:

      A (-2, 6)
      B (-5, 7)
      C (-4, 4)

      * Please note that the process is a bit simpler than in the video because the line of reflection is the actual y-axis. If the line of reflection was something else (like x = -4), you would need to do more than just taking the negative of the x-value - the process would be similar to what Sal does in the video.

      Hope this helps!
      (9 votes)
  • male robot johnny style avatar for user mohidafzal31
    I can't seem to find it anywhere, but one of the questions in a worksheet given by my teacher, we are asked to:
    Reflect at "y = -x"
    Is there a video or exercise on this that I missed? if not then pls guide me
    (6 votes)
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  • mr pants orange style avatar for user bhudson642
    Why is there nothing on dilation in this playlist? It's the only type of transformation not covered,
    (3 votes)
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  • primosaur seed style avatar for user Anna Maxwell
    So was that reflection a reflection across the y-axis?
    (2 votes)
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  • orange juice squid orange style avatar for user Latoyia Timmons
    is there a specific reason as to why u would put half of the total number of spaces ?
    (3 votes)
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  • winston default style avatar for user Ryan Wilson
    How do you explain if there is or is not a line of refection
    (3 votes)
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  • aqualine ultimate style avatar for user PumpkinPi_3🎃
    Hi there! I have a difficult math question that reads:

    "Perform a reflection on the figure below across the line of reflection Y."
    I have to plot out the 'reflection' of a triangle.
    I have tried to solve this problem more than *3 times.*
    (2 votes)
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    • leaf green style avatar for user kubleeka
      Reflections will turn a straight line into another straight line, as will all rigid transformations. So if you want to reflect a line segment, it's enough to reflect the endpoints and draw a line between them. For your triangle, you need only compute the reflection on the vertices.

      To reflect across line Y, find the line through your chosen point perpendicular to Y, and find the length of the segment from your point to Y. Your reflected point will land that distance from Y, on the other side, in line with the segment you found.
      (3 votes)
  • blobby green style avatar for user s5302599
    Reflecting across a graph,does the Y always stay the same?
    (2 votes)
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  • aqualine sapling style avatar for user Aryanna Cortez
    Do you know any tricks or like an easier way to find reflections?
    (2 votes)
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    • duskpin ultimate style avatar for user The Bibliophile
      I use a memorization trick. Let's say you are given the point (2, -7).
      To reflect across the x-axis, use the rule (x, -y). This will give you (2, 7).
      To reflect across the y-axis, use the rule (-x, y). This gives you (-2, -7).
      To reflect across the line y=x, use the rule (y, x). This gives you (-7, 2).
      To reflect across the line y=-x, use the rule (-y, -x). This gives you (7, -2).

      Just memorize these formulas and you'll be good. You don't have to graph a point to find its reflection point.

      Hope this helps :D
      (2 votes)

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.