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U9L2 Reflections Notes: Exploring Vertical and Horizontal Lines

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Bianca Stratford

2/4/2023

Geometry

U9L2 Reflections Notes

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Geometry

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Tranformations & translations

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Symmetry

U9L2 Reflections Notes: Exploring Vertical and Horizontal Lines

A comprehensive guide to reflecting in vertical and horizontal lines covering key concepts, rules, and practical examples of geometric transformations.

• The guide explains horizontal reflection and vertical reflection through detailed examples and coordinates
• Covers reflections over x-axis, y-axis, and other lines including y=x and y=-x
• Includes practical exercises with various geometric shapes like triangles, rectangles, and parallelograms
• Features methods for identifying the line of reflection and working with coordinates

...

2/4/2023

355

<h2 id="rules">Rules</h2> <p>When reflecting a point over the x-axis, the new coordinates of the point (x₁,y) become (x₁,-y). On the other

View

Page 2: Advanced Reflection Lines

This page expands on reflection concepts by introducing reflections over vertical lines other than the y-axis and horizontal lines other than the x-axis, as well as diagonal reflections.

Vocabulary: The line y=x is a diagonal line that serves as a line of reflection, creating a unique type of transformation.

Example: For reflection over y=x, the rule x,yx,y = y,xy,x is applied, swapping x and y coordinates.

The page includes six detailed examples:

  • Triangle JKL reflection over x=4
  • Square RSTU reflection over x=-1
  • Parallelogram CDEF reflection over y=2
  • Triangle MNP reflection over y=-5
  • Triangle XYZ reflection over y=x
  • Rectangle GHIJ reflection over y=x
<h2 id="rules">Rules</h2> <p>When reflecting a point over the x-axis, the new coordinates of the point (x₁,y) become (x₁,-y). On the other

View

Page 3: Line of Reflection Identification

This page focuses on identifying lines of reflection and working with the line y=-x as a reflection line. It emphasizes practical problem-solving techniques.

Highlight: Finding the midpoint between corresponding points can help identify the line of reflection.

Example: For reflection over y=-x, the rule x,yx,y = −y,−x-y,-x is applied.

The page includes:

  • Square ABCD reflection over y=-x
  • Triangle STU reflection over y=-x
  • Six exercises for identifying various lines of reflection including y-axis, x-axis, y=x, and specific vertical and horizontal lines

Definition: The line of reflection is the line that acts as a mirror, creating a symmetrical image of the original shape.

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Subjects

Geometry

Tranformations & translations

Symmetry

 

Geometry

•

355

•

Feb 4, 2023

•

3 pages

U9L2 Reflections Notes: Exploring Vertical and Horizontal Lines

user profile picture

Bianca Stratford

@biancastratford

A comprehensive guide to reflecting in vertical and horizontal lines covering key concepts, rules, and practical examples of geometric transformations.

• The guide explains horizontal reflection and vertical reflection through detailed examples and coordinates
• Covers reflections over x-axis, y-axis,... Show more

<h2 id="rules">Rules</h2> <p>When reflecting a point over the x-axis, the new coordinates of the point (x₁,y) become (x₁,-y). On the other

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Page 2: Advanced Reflection Lines

This page expands on reflection concepts by introducing reflections over vertical lines other than the y-axis and horizontal lines other than the x-axis, as well as diagonal reflections.

Vocabulary: The line y=x is a diagonal line that serves as a line of reflection, creating a unique type of transformation.

Example: For reflection over y=x, the rule x,yx,y = y,xy,x is applied, swapping x and y coordinates.

The page includes six detailed examples:

  • Triangle JKL reflection over x=4
  • Square RSTU reflection over x=-1
  • Parallelogram CDEF reflection over y=2
  • Triangle MNP reflection over y=-5
  • Triangle XYZ reflection over y=x
  • Rectangle GHIJ reflection over y=x

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Page 3: Line of Reflection Identification

This page focuses on identifying lines of reflection and working with the line y=-x as a reflection line. It emphasizes practical problem-solving techniques.

Highlight: Finding the midpoint between corresponding points can help identify the line of reflection.

Example: For reflection over y=-x, the rule x,yx,y = −y,−x-y,-x is applied.

The page includes:

  • Square ABCD reflection over y=-x
  • Triangle STU reflection over y=-x
  • Six exercises for identifying various lines of reflection including y-axis, x-axis, y=x, and specific vertical and horizontal lines

Definition: The line of reflection is the line that acts as a mirror, creating a symmetrical image of the original shape.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Basic Reflection Concepts and Rules

This page introduces fundamental concepts of reflection in mathematics, focusing on the x-axis and y-axis reflections. The content includes essential rules and multiple examples of reflecting different shapes.

Definition: A reflection is a flip over a line called the line of reflection, where each point and its image are equidistant from the reflection line.

Highlight: Reflection is classified as a rigid motion, preserving the shape and size of the original figure.

Example: When reflecting over the x-axis, the rule x1,yx₁,y = x1,−yx₁,-y is applied, while for y-axis reflection, the rule is x1,yx₁,y = −x1,y-x₁,y.

The page demonstrates practical applications through four main examples:

  • Triangle ABC reflection over x-axis
  • Rectangle PORS reflection over y-axis
  • Trapezoid FGHI reflection over y-axis
  • Rhombus WXYZ reflection over x-axis

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

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Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

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Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user