Questions and Answers
What is a dilation?
What is the center of dilation?
The point of intersection of lines through each pair of corresponding vertices in a dilation.
Define the scale factor.
The ratio used to enlarge or reduce similar figures.
What does 'congruent' mean?
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What is a translation?
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What does reflection mean in geometry?
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What is rotation in geometry?
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What is a transformation?
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A 360° rotation changes the coordinates of a point.
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What is a 90° rotation clockwise transformation?
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What is the reflection across the x-axis transformation?
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What is the reflection across the y-axis transformation?
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What does similarity mean in geometry?
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What does a dilation enlargement with a scale factor greater than 1 indicate?
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What does a dilation reduction with a scale factor less than 1 indicate?
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What is the pre-image in a transformation?
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What is the image in a transformation?
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Study Notes
Dilation and Transformations
- Dilation is a transformation that alters the size of a figure, either enlarging or reducing it.
- Enlargement increases all dimensions proportionately, while reduction decreases all dimensions in the same ratio.
- The center of dilation is the intersection point from lines drawn between corresponding vertices of the original and transformed figures.
- Scale factor indicates the ratio used for enlarging or reducing figures.
Geometric Transformations
- Congruent figures have identical size and shape, crucial for understanding transformations.
- Translation refers to the sliding of a figure in a specified direction by a uniform distance.
- Reflection is when a figure is flipped over a predefined line, also known as a mirror line.
- Rotation involves turning a figure around a specific point by a set angle (e.g., 90°, 180°, 270°, 360°).
Properties of Transformations
- A 360° rotation results in coordinates that remain unchanged.
- Scaling describes the ratio between two measurement sets, important for understanding size changes.
- Different types of reflections alter coordinates:
- Reflection across the x-axis transforms (x,y) to (x,-y).
- Reflection across the y-axis changes (x,y) to (-x,y).
- Reflection across the origin results in (x,y) becoming (-x,-y).
Dilation Types
- Dilation enlargement can be represented as (x,y) transforming to (2x, 2y) or (4x, 4y) with a scale factor greater than 1.
- Dilation reduction transforms coordinates like (x,y) to (.5x, .5y) or (1/2x, 1/2y) with a scale factor less than 1.
Similarity and Transformation Concepts
- Similar shapes share the same form but differ in dimension.
- An image is the resultant set of points after applying a transformation, denoted as (p', r', x').
- The pre-image is the figure prior to transformation, marked as (p, r, x).
- Transformation specific effects on rotation include:
- 90-degree clockwise: (x,y) → (y,-x)
- 90-degree counterclockwise: (x,y) → (-y,x)
- 180-degree: (x,y) → (-x,-y)
- 270-degree clockwise: (x,y) → (-y,x)
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Description
Explore key concepts in geometry with our flashcards on dilation, enlargement, reduction, and the center of dilation. Perfect for students looking to understand these transformations better. Test your knowledge and reinforce your learning!
