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## 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

CCSS.Math:

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

## Want to join the conversation?

- are there any tricks or rules with rigid transformations?(20 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.(3 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!(9 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(6 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,(3 votes)
- there is, just keep going down, it's the third to last group in this playlist(4 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!(4 votes)

- is there a specific reason as to why u would put half of the total number of spaces ?(3 votes)
- If it is 6 spaces the line divides it by too, that's my understanding.(1 vote)

- How do you explain if there is or is not a line of refection(3 votes)
- 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)- 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)

- Reflecting across a graph,does the Y always stay the same?(2 votes)
- The y only stays the same if it is reflected across the y-axis, otherwise it will change.(2 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(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.