Questions and Answers
What transformation is represented by (x,y) = (x,-y)?
What transformation is represented by (x,y) = (-x,y)?
What transformation is represented by (x,y) = (-y,x)?
What transformation is represented by (x,y) = (y,-x)?
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What transformation is represented by (x,y) = (-x,-y)?
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What transformation is represented by (x,y) = (x + a, y + b)?
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Describe the transformation represented by the points (2,5) = (4,2) and (7,9) = (9,6).
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Describe the transformation represented by (7, 8) = (7, -8).
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Describe the transformation represented by (-1,-4) = (1, -4).
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Describe the transformation represented by (-5,-12) = (12,-5).
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Describe the transformation represented by (10, -2) = (-2,-10).
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Describe the transformation represented by (3,-11) = (-3, 11).
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Describe the transformation represented by (-4,5) = (-11,9).
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Describe the transformation represented by (-19,-5) = (-19,5).
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Describe the transformation represented by (-12, -10) = (12, -10).
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Describe the transformation represented by (-1,-2) = (2,-1).
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Describe the transformation represented by (-8,-6) = (-6,8).
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Describe the transformation represented by (-13, -5) = (13,5).
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What is the result of transforming (-7,4) Translated 3 units left and 5 units up?
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What is the result of transforming (-1,1) Reflected over the x-axis?
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What is the result of transforming (0,-3) Reflected over the y-axis?
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What is the result of transforming (-2,5) Rotated 90 degrees counterclockwise about the origin?
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What is the result of transforming (-7,11) Rotated 90 degrees clockwise about the origin?
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What is the result of transforming (15,0) Rotated 180 degrees about the origin?
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What is the result of transforming (4,-8) dilated by a scale factor of ½?
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Describe the transformation represented by (-3,7) = (-9,21).
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What is the result of transforming (0,5) dilated by a scale factor of 6?
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What is the result of transforming (12, 4) dilated by a scale factor of ¾?
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Do dilations produce images similar or congruent to the pre-image?
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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
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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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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.
