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Questions and Answers
A ______ motion preserves the distance and angles between points.
A ______ motion preserves the distance and angles between points.
rigid
The transformation represented by 𝑅(180°,𝑂) involves a rotation of ______ degrees.
The transformation represented by 𝑅(180°,𝑂) involves a rotation of ______ degrees.
180
The reflection across the line 𝑟𝑥=1 is a type of ______.
The reflection across the line 𝑟𝑥=1 is a type of ______.
reflection
The coordinates of point 𝐴 after the transformation 𝑇〈2,3〉 would be shifted by ______ units in the x-direction and ______ units in the y-direction.
The coordinates of point 𝐴 after the transformation 𝑇〈2,3〉 would be shifted by ______ units in the x-direction and ______ units in the y-direction.
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A composition of transformations includes more than one transformation, such as a translation followed by a ______.
A composition of transformations includes more than one transformation, such as a translation followed by a ______.
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When writing the equation of the line of reflection, it can be expressed in - form.
When writing the equation of the line of reflection, it can be expressed in - form.
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A shape has rotational symmetry if it can be rotated less than ______ degrees and look the same.
A shape has rotational symmetry if it can be rotated less than ______ degrees and look the same.
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If a figure has no lines of symmetry, we state that there are ______ lines of symmetry.
If a figure has no lines of symmetry, we state that there are ______ lines of symmetry.
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Study Notes
Rigid Motions
- Rigid motions preserve the size and shape of figures.
- Transformations that result in rigid motions include reflections, rotations, and translations.
Rotations
- Rotations involve turning a figure around a fixed point (the center of rotation).
- Rotations are described by the angle of rotation and the center of rotation. Specific angles and centers are given in exercises.
Coordinates of Image Points
- Coordinates of rotated image points can be calculated based on the given rotation rules.
- Points are plotted, and the coordinates of the corresponding image are noted.
Finding Pre-Images
- Given the coordinates of the image of a point, the coordinates of the pre-image can be determined based on the transformation.
- Finding a pre-image involves reversing the transformation process. For example, if T(2,3), reverse (opposite) calculation
Reflections
- Reflections involve flipping a figure over a line (the line of reflection).
- Reflections are described by the line of reflection.
- The exercises provide specific lines and shapes to reflect.
Vector Components
- Vectors have a magnitude and direction indicated by their components.
- Given a vector or series of components, the resultant vector or the coordinates of the image are evaluated.
Line of Reflection Equation
- The specific example provides points to calculate the equation of the line of reflection.
Compositions of Transformations
- Compositions involve performing more than one transformation in sequence on a shape.
- Order of transformation(s) matters, so order is important to follow. Complex compositions that involve multiple transformations on a shape are presented in the exercises, such as:
- (translation) followed by (reflection)*
- (rotation) followed by (translation)*
Rotational Symmetry
- Rotational symmetry occurs if a figure can be rotated around a point and appear the same after the rotation.
- The smallest angle of rotation that produces this is listed.
Lines of Symmetry
- Lines of symmetry divide a figure into two identical halves.
- Figures with lines of symmetry are identified.
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Description
Test your understanding of rigid motions, including reflections, rotations, and translations. This quiz covers how to calculate coordinates of image points and find pre-images based on transformations. Get ready to apply your knowledge of geometry concepts!
