Transformations Overview in Geometry
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Questions and Answers

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

  • Rotation 90 degrees counterclockwise about the origin
  • Rotation 180 degrees about the origin
  • Reflection over the y-axis
  • Reflection over the x-axis (correct)

    • What transformation is represented by (x,y) = (-x,y)?

  • Reflection over the x-axis
  • Translation
  • Rotation 90 degrees counterclockwise about the origin
  • Reflection over the y-axis (correct)

    • What transformation is represented by (x,y) = (-y,x)?

  • Reflection over the x-axis
  • Dilation
  • Rotation 90 degrees clockwise about the origin
  • Rotation 90 degrees counterclockwise about the origin (correct)

    • What transformation is represented by (x,y) = (y,-x)?

    <p>Rotation 90 degrees clockwise about the origin</p> Signup and view all the answers

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

    <p>Rotation 180 degrees about the origin</p> Signup and view all the answers

    What transformation is represented by (x,y) = (x + a, y + b)?

    <p>Translation</p> Signup and view all the answers

    Describe the transformation represented by the points (2,5) = (4,2) and (7,9) = (9,6).

    <p>Translation right 2 units and down 3 units.</p> Signup and view all the answers

    Describe the transformation represented by (7, 8) = (7, -8).

    <p>Reflection over the x-axis.</p> Signup and view all the answers

    Describe the transformation represented by (-1,-4) = (1, -4).

    <p>Reflection over the y-axis.</p> Signup and view all the answers

    Describe the transformation represented by (-5,-12) = (12,-5).

    <p>Rotation 90 degrees counterclockwise about the origin.</p> Signup and view all the answers

    Describe the transformation represented by (10, -2) = (-2,-10).

    <p>Rotation 90 degrees clockwise about the origin.</p> Signup and view all the answers

    Describe the transformation represented by (3,-11) = (-3, 11).

    <p>Rotation 180 degrees about the origin.</p> Signup and view all the answers

    Describe the transformation represented by (-4,5) = (-11,9).

    <p>Translation left 7 units and up 4 units.</p> Signup and view all the answers

    Describe the transformation represented by (-19,-5) = (-19,5).

    <p>Reflection over the x-axis.</p> Signup and view all the answers

    Describe the transformation represented by (-12, -10) = (12, -10).

    <p>Reflection over the y-axis.</p> Signup and view all the answers

    Describe the transformation represented by (-1,-2) = (2,-1).

    <p>Rotation 90 degrees counterclockwise about the origin.</p> Signup and view all the answers

    Describe the transformation represented by (-8,-6) = (-6,8).

    <p>Rotation 90 degrees clockwise about the origin.</p> Signup and view all the answers

    Describe the transformation represented by (-13, -5) = (13,5).

    <p>Rotation 180 degrees about the origin.</p> Signup and view all the answers

    What is the result of transforming (-7,4) Translated 3 units left and 5 units up?

    <p>(-10,9).</p> Signup and view all the answers

    What is the result of transforming (-1,1) Reflected over the x-axis?

    <p>(-1,-1).</p> Signup and view all the answers

    What is the result of transforming (0,-3) Reflected over the y-axis?

    <p>(0,-3).</p> Signup and view all the answers

    What is the result of transforming (-2,5) Rotated 90 degrees counterclockwise about the origin?

    <p>(-5,-2).</p> Signup and view all the answers

    What is the result of transforming (-7,11) Rotated 90 degrees clockwise about the origin?

    <p>(11,7).</p> Signup and view all the answers

    What is the result of transforming (15,0) Rotated 180 degrees about the origin?

    <p>(-15,0).</p> Signup and view all the answers

    What is the result of transforming (4,-8) dilated by a scale factor of ½?

    <p>(2,-4).</p> Signup and view all the answers

    Describe the transformation represented by (-3,7) = (-9,21).

    <p>Dilation by a scale factor of 3.</p> Signup and view all the answers

    What is the result of transforming (0,5) dilated by a scale factor of 6?

    <p>(0,30).</p> Signup and view all the answers

    What is the result of transforming (12, 4) dilated by a scale factor of ¾?

    <p>(9,3).</p> Signup and view all the answers

    Do dilations produce images similar or congruent to the pre-image?

    <p>Similar</p> Signup and view all the answers

    Study Notes

    Transformations Overview

    • Transformation rules dictate how points in a coordinate system move under various operations.
    • Each transformation alters the coordinates of a point (x,y) based on specific mathematical rules.

    Reflection Transformations

    • Reflection over the x-axis: (x,y) transforms to (x,-y).
    • Reflection over the y-axis: (x,y) transforms to (-x,y).

    Rotation Transformations

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

    Translation Transformation

    • Translation: (x,y) transforms to (x + a, y + b) indicating a shift by (a,b) units.
    • Example of translation: (2,5) to (4,2) indicates a move right by 2 units and down by 3.

    Specific Transformation Examples

    • Point (7, 8) reflected over the x-axis results in (7, -8).
    • Point (-1, -4) reflected over the y-axis results in (1, -4).
    • Point (-5, -12) rotated 90 degrees counterclockwise results in (12, -5).
    • Point (10, -2) rotated 90 degrees clockwise results in (-2, -10).
    • Point (3, -11) rotated 180 degrees yields (-3, 11).

    Dilation Transformations

    • Dilation by a scale factor alters the size of a shape while keeping the same proportions.
      • Example: Dilation of (-3,7) yields (-9,21) when scaled by 3.
      • Dilation does not preserve congruency but produces similar images.
    • Dilation by a scale factor of ½ transforms (4,-8) to (2,-4).
    • Dilation by a scale factor of 6 transforms (0,5) to (0,30).

    Summary of Reflection, Rotation, and Dilation

    • Reflections yield images that are mirror images across a given axis.
    • Rotations change the position of points based on an angular transformation around the origin.
    • Dilations maintain the shape's angles but alter dimensions based on the scale factor.

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    Quiz Team

    Description

    Explore the various types of transformations in geometry, including reflection, rotation, and translation. This quiz covers the mathematical rules and examples for each type of transformation, focusing on how coordinates change under these operations.

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