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Geometric Transformations Quiz

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Questions and Answers

What is the transformation represented by (x,y) --> (x+5, y+7)?

Rotation 90 degrees clockwise

Dilation by a scale factor of 3

Reflection over the x-axis

Translation right 5, up 7 (correct)

What is the transformation represented by (x,y) --> (x-2, y-6)?

Reflection over the y-axis

Dilation by a scale factor of 1/2

Rotation 180 degrees

Translation left 2, down 6 (correct)

What is the transformation represented by (x,y) --> (x, -y)?

Reflection over the x-axis (correct)

Translation

Dilation by a scale factor of 3

Rotation 90 degrees counterclockwise

What is the transformation represented by (x,y) --> (-y, x)?

Rotation 90 degrees clockwise Signup and view all the answers

What is represented by the term 'isometric slide'?

Translation Signup and view all the answers

What is the transformation represented by (x,y) --> (3x, 3y)?

Dilation by a scale factor of 3 Signup and view all the answers

What is the transformation represented by (x,y) --> (-x, y)?

Reflection over the y-axis Signup and view all the answers

What is the transformation represented by (x,y) --> (-x, -y)?

Rotation 180 degrees Signup and view all the answers

What is the transformation represented by (x,y) --> (x/2, y/2)?

Dilation by a scale factor of 1/2 Signup and view all the answers

What is the transformation represented by (x,y) --> (y, x)?

Reflection over the line y = x Signup and view all the answers

What does 'isometric flip' refer to?

Reflection Signup and view all the answers

What does 'isometric turn' refer to?

Rotation Signup and view all the answers

What does 'stretch or shrink' refer to?

Dilation Signup and view all the answers

Study Notes

Translations

Translation right 5, up 7: Moves a point (x,y) to (x+5, y+7).
Translation left 2, down 6: Moves a point (x,y) to (x-2, y-6).

Reflections

Reflection over the x-axis: Changes the point (x,y) to (x, -y).
Reflection over the y-axis: Changes the point (x,y) to (-x, y).
Reflection over the line y = x: Swaps coordinates, changing (x,y) to (y, x).
Reflection over the line y = -x: Inverts both coordinates, changing (x,y) to (-y, -x).

Rotations

Rotation 90 degrees clockwise: Changes (x,y) to (y, -x).
Rotation 90 degrees counterclockwise: Changes (x,y) to (-y, x).
Rotation 180 degrees: Changes (x,y) to (-x, -y).

Dilations

Dilation by a scale factor of 3: Enlarges a point (x,y) to (3x, 3y).
Dilation by a scale factor of 1/2: Reduces a point (x,y) to (x/2, y/2).

Geometric Transformations

Translation: Described as an isometric slide, maintains shape and size.
Reflection: Defined as an isometric flip, maintains size while changing orientation.
Rotation: Described as an isometric turn, maintains distances and angles.
Dilation: Defined as a stretch or shrink, alters size while maintaining proportion.

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Description

Test your knowledge of geometric transformations including translations, reflections, rotations, and dilations. This quiz covers how to apply these transformations to points in a coordinate plane. Perfect for geometry students looking to reinforce their understanding.