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### Course: 8th grade (Eureka Math/EngageNY) > Unit 2

Lesson 1: Topic A: Definitions and properties of the basic rigid motions- Introduction to geometric transformations
- Identifying transformations
- Identify transformations
- Translations intro
- Translating points
- Translate points
- Translating shapes
- Translating shapes
- Translate shapes
- Determining translations
- Determine translations
- Rotations intro
- Rotating points
- Rotate points (basic)
- Determining rotations
- Determine rotations (basic)
- Reflecting points
- Reflect points
- Reflecting shapes
- Reflecting shapes
- Reflect shapes
- Determining reflections
- Determine reflections
- Translations review
- Rotations review
- Reflections review

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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.

## Want to join the conversation?

- are there any tricks or rules with rigid transformations?(21 votes)
- I can't think of any tricks, but I do know a rule:

A rigid transformation only occours if the 2nd image of the shape preserves distance between points, and preserves the angle measure of the lines.(17 votes)

- How do change figure across the y-axis(6 votes)
- 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)

- 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)
- Yes, you can do it that way, although you probably figured that out by now because it's been 4 years.(2 votes)

- 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)- *Nevermind, punching y = -x into desmos gave me the line of reflection!*(6 votes)

- Why is there nothing on dilation in this playlist? It's the only type of transformation not covered,(4 votes)
- there is, just keep going down, it's the third to last group in this playlist(7 votes)

- Do you know any tricks or like an easier way to find reflections?(2 votes)
- 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)

- i didn't understand(3 votes)
- 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)

- what if the line of reflection os oblique? is there a general rule for the points?(3 votes)
- 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)

- So was that reflection a reflection across the y-axis?(2 votes)
- No, It would be a reflection across something on the x-axis.

Hope that helps!(5 votes)

- why is math soooooo hard!(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.