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Fun with Reflection and Translation in Geometry: Worksheets & Examples for Kids

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Fun with Reflection and Translation in Geometry: Worksheets & Examples for Kids
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Colleensasser

@colleeflowerr

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Understanding rigid motion in geometry and transformations - a comprehensive guide covering reflections, translations, and rotations with detailed examples and rules.

  • Rigid motions preserve both length and angle measurements while transforming geometric figures
  • Reflections involve flipping figures across a line of reflection, maintaining equal distances
  • Translations involve sliding figures horizontally and/or vertically using coordinate rules
  • Rotations involve turning figures around a fixed point using specific angle measurements
  • Each transformation type follows distinct rules and formulas for calculating new coordinates

10/24/2023

449

<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

View

Page 3: Complex Reflections

This page covers more advanced reflection examples, particularly focusing on diagonal reflections and their rules.

Example: For reflection across y=-x:

  • Point S(-1,-6) becomes S'(6,1)
  • Point T(0,-3) becomes T'(3,0)
  • Point U(3,-4) becomes U'(4,-3)

Highlight: When reflecting across y=-x, coordinates switch places and change signs.

<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

View

Page 8: Rotations Around Points

This page explains how to perform rotations around points other than the origin.

Definition: Four-step process for rotating around a point:

  1. Write original points
  2. Subtract point of rotation
  3. Apply rotation rules
  4. Add back point of rotation

Example: 180° rotation around point (1,1):

  • Original point F(1,2)
  • Subtract (1,1): (0,1)
  • Apply rotation: (0,-1)
  • Add (1,1): F'(1,0)
<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

View

Page 7: Advanced Rotations

This page explores more complex rotation examples and combinations with other transformations.

Example: 270° rotation about the origin:

  • Point A(2,7) becomes A'(-7,2)
  • Point B(6,5) becomes B'(-5,6)

Highlight: Multiple transformations can be combined, such as translation followed by rotation or reflection followed by rotation.

<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

View

Page 6: Introduction to Rotations

This page introduces rotation as a rigid motion, focusing on rotations around the origin.

Definition: Rotation rules around the origin:

  • 90° CCW: (x,y) → (-y,x)
  • 180°: (x,y) → (-x,-y)
  • 270° CCW: (x,y) → (y,-x)

Example: 90° rotation about the origin:

  • Point A(3,5) becomes A'(-5,3)
  • Point B(1,7) becomes B'(-7,1)
<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

View

Page 9: Final Rotation Examples

This page provides additional examples of rotations around specific points.

Example: 90° CCW rotation around point (0,1):

  • Point G(-3,-2) becomes G'(3,-2)
  • Point F(-3,-5) becomes F'(6,-2)
  • Point H(0,-1) becomes H'(7,1)

Highlight: The process demonstrates how complex rotations can be broken down into manageable steps using coordinate geometry.

<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

View

Page 5: Composition of Transformations

This page explores how multiple transformations can be combined.

Definition: A composition of rigid motions involves applying two or more transformations sequentially.

Example: Reflecting across x-axis followed by translation T<9,-1>:

  • Point X(-3,1) becomes X'(-3,-1) then X"(6,-8)
  • Point Y(-2,1) becomes Y'(-2,-1) then Y"(7,-2)

Highlight: When combining transformations, the order of operations matters and affects the final result.

<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

View

Page 1: Introduction to Reflections

This page introduces the fundamental concepts of rigid motion in geometry and reflections. A reflection involves flipping a figure across a line while maintaining equal distances from the line of reflection.

Definition: A rigid motion is a transformation that preserves both length and angle measurements.

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

Example: When reflecting point A(-4,2) across the x-axis, its image becomes A'(-4,-2), demonstrating how the y-coordinate changes sign while the x-coordinate remains the same.

Highlight: Common lines of reflection include:

  • x-axis and y-axis
  • Vertical lines (x=a) and horizontal lines (y=b)
  • Diagonal lines (y=x or y=-x)
<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

View

Page 4: Introduction to Translations

This page introduces translations as another type of rigid motion.

Definition: A translation is a transformation that slides a figure vertically and/or horizontally without changing its size or shape.

Vocabulary: Translation notation: (x,y) → (x+h, y+k) or <h,k>

  • h represents horizontal shift
  • k represents vertical shift

Example: Translation T<5,7>:

  • Point D(-3,3) becomes D'(4,7)
  • Point E(0,2) becomes E'(7,6)
  • Point F(-1,-3) becomes F'(6,7)
<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

View

Page 2: Advanced Reflection Examples

This page expands on reflection concepts with multiple examples across different lines of reflection.

Example: When reflecting across x=4:

  • Point J(1,-1) becomes J'(7,-1)
  • Point K(2,3) becomes K'(6,3)
  • Point L(3,-2) becomes L'(5,-2)

Highlight: Key rules for different reflection lines:

  • For x=a line: y-coordinate stays the same
  • For y=b line: x-coordinate stays the same
  • For y=x line: x and y coordinates switch places

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Subjects

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Geometry

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Dilations

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Dilations

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Dilations: scale factor

Fun with Reflection and Translation in Geometry: Worksheets & Examples for Kids

user profile picture

Colleensasser

@colleeflowerr

·

16 Followers

Follow

Understanding rigid motion in geometry and transformations - a comprehensive guide covering reflections, translations, and rotations with detailed examples and rules.

  • Rigid motions preserve both length and angle measurements while transforming geometric figures
  • Reflections involve flipping figures across a line of reflection, maintaining equal distances
  • Translations involve sliding figures horizontally and/or vertically using coordinate rules
  • Rotations involve turning figures around a fixed point using specific angle measurements
  • Each transformation type follows distinct rules and formulas for calculating new coordinates

10/24/2023

449

 

10th

 

Geometry

49

<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

Page 3: Complex Reflections

This page covers more advanced reflection examples, particularly focusing on diagonal reflections and their rules.

Example: For reflection across y=-x:

  • Point S(-1,-6) becomes S'(6,1)
  • Point T(0,-3) becomes T'(3,0)
  • Point U(3,-4) becomes U'(4,-3)

Highlight: When reflecting across y=-x, coordinates switch places and change signs.

<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

Page 8: Rotations Around Points

This page explains how to perform rotations around points other than the origin.

Definition: Four-step process for rotating around a point:

  1. Write original points
  2. Subtract point of rotation
  3. Apply rotation rules
  4. Add back point of rotation

Example: 180° rotation around point (1,1):

  • Original point F(1,2)
  • Subtract (1,1): (0,1)
  • Apply rotation: (0,-1)
  • Add (1,1): F'(1,0)
<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

Page 7: Advanced Rotations

This page explores more complex rotation examples and combinations with other transformations.

Example: 270° rotation about the origin:

  • Point A(2,7) becomes A'(-7,2)
  • Point B(6,5) becomes B'(-5,6)

Highlight: Multiple transformations can be combined, such as translation followed by rotation or reflection followed by rotation.

<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

Page 6: Introduction to Rotations

This page introduces rotation as a rigid motion, focusing on rotations around the origin.

Definition: Rotation rules around the origin:

  • 90° CCW: (x,y) → (-y,x)
  • 180°: (x,y) → (-x,-y)
  • 270° CCW: (x,y) → (y,-x)

Example: 90° rotation about the origin:

  • Point A(3,5) becomes A'(-5,3)
  • Point B(1,7) becomes B'(-7,1)
<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

Page 9: Final Rotation Examples

This page provides additional examples of rotations around specific points.

Example: 90° CCW rotation around point (0,1):

  • Point G(-3,-2) becomes G'(3,-2)
  • Point F(-3,-5) becomes F'(6,-2)
  • Point H(0,-1) becomes H'(7,1)

Highlight: The process demonstrates how complex rotations can be broken down into manageable steps using coordinate geometry.

<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

Page 5: Composition of Transformations

This page explores how multiple transformations can be combined.

Definition: A composition of rigid motions involves applying two or more transformations sequentially.

Example: Reflecting across x-axis followed by translation T<9,-1>:

  • Point X(-3,1) becomes X'(-3,-1) then X"(6,-8)
  • Point Y(-2,1) becomes Y'(-2,-1) then Y"(7,-2)

Highlight: When combining transformations, the order of operations matters and affects the final result.

<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

Page 1: Introduction to Reflections

This page introduces the fundamental concepts of rigid motion in geometry and reflections. A reflection involves flipping a figure across a line while maintaining equal distances from the line of reflection.

Definition: A rigid motion is a transformation that preserves both length and angle measurements.

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

Example: When reflecting point A(-4,2) across the x-axis, its image becomes A'(-4,-2), demonstrating how the y-coordinate changes sign while the x-coordinate remains the same.

Highlight: Common lines of reflection include:

  • x-axis and y-axis
  • Vertical lines (x=a) and horizontal lines (y=b)
  • Diagonal lines (y=x or y=-x)
<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

Page 4: Introduction to Translations

This page introduces translations as another type of rigid motion.

Definition: A translation is a transformation that slides a figure vertically and/or horizontally without changing its size or shape.

Vocabulary: Translation notation: (x,y) → (x+h, y+k) or <h,k>

  • h represents horizontal shift
  • k represents vertical shift

Example: Translation T<5,7>:

  • Point D(-3,3) becomes D'(4,7)
  • Point E(0,2) becomes E'(7,6)
  • Point F(-1,-3) becomes F'(6,7)
<h2 id="reflections">Reflections</h2> <h3 id="vocabulary">Vocabulary</h3> <ul> <li>A rigid motion is a transformation that preserves length

Page 2: Advanced Reflection Examples

This page expands on reflection concepts with multiple examples across different lines of reflection.

Example: When reflecting across x=4:

  • Point J(1,-1) becomes J'(7,-1)
  • Point K(2,3) becomes K'(6,3)
  • Point L(3,-2) becomes L'(5,-2)

Highlight: Key rules for different reflection lines:

  • For x=a line: y-coordinate stays the same
  • For y=b line: x-coordinate stays the same
  • For y=x line: x and y coordinates switch places

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Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying