Geometry Transformations Flashcards

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)