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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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  • blobby green style avatar for user ramona.spencer
    are there any tricks or rules with rigid transformations?
    (21 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!
      (14 votes)
  • primosaur ultimate style avatar for user Mohammad Zayd
    I have a question. To find the line of reflection for a triangle, could someone count all the spaces between the two same vertices and then divide them by two. Then add that quotient to a vertice. One example could be in the video. The distance between Triangle ABC's vertice of C and Triangle A'B'C''s vertice of C is six. So then divide six by two to get 3. Then add that 3 to Triangle A'B'C' vertice c's Y-coordinate to get 1. The line of reflection is on the Y-coordinate of 1. Sorry if this was a little confusing. It is difficult to type about Triangle A'B'C' and the different vertices. Sorry.
    (8 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,
    (4 votes)
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  • 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
    (5 votes)
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  • marcimus purple 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 Telepath
      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
      (6 votes)
  • sneak peak green style avatar for user zaksab1
    i didn't understand
    (3 votes)
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    • blobby blue style avatar for user joshua
      Please specify what you didn't understand. To do reflection for a shape, simply reflect each point respectively, last connect it, forming the reflected shape.

      To know where do you place the reflected point, simply count how many unit(s) is there from that initial point to the line of reflection. Then place the point on the other side of the line of reflection with the same number of unit(s).
      (5 votes)
  • sneak peak yellow style avatar for user Anderson Adoral
    what if the line of reflection os oblique? is there a general rule for the points?
    (3 votes)
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    • male robot donald style avatar for user Venkata
      One thing you could do is this: Consider the point given and the line of reflection (which is oblique). Now, draw a line from the point till you intersect the line of reflection. After you intersect it, draw a line perpendicular to the line you just drew, but make sure that this line is equal in length to the first line. Where your second line stops is the reflection of the point.

      Observe that the idea here is to make a square with the point as one corner and the line of reflection as the diagonal.
      (5 votes)
  • primosaur seed style avatar for user Anna Maxwell
    So was that reflection a reflection across the y-axis?
    (2 votes)
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  • blobby green style avatar for user MartiW
    the dang volume isn't working, so, I am confused on what's happening. Please help me with this!
    (2 votes)
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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.