Chapter 1
Numbers and Operations
Course: Gace Middle Grades Math 4 8 704
Subject: Gace Middle Grades Math 4 8 704
Chapter: Geometry And Measurement
A transformation is a change in the position, size, or orientation of a geometric figure in the plane. Transformations are divided into two main types:
- Rigid transformations (translations, reflections, rotations) which preserve distance and angle measure, meaning the preimage and image are congruent.
- Non-rigid transformations (dilations) which preserve shape and angle measures but change size, creating figures that are similar but not necessarily congruent.
Transformations are often described in terms of mappings from the original figure (preimage) to the new figure (image).
1. Applies properties of translations, reflections, and rotations
Translations
A translation moves every point of a figure the same distance in the same direction. This means the figure slides without rotating, flipping, or changing size.
- Properties: line segments map to congruent line segments, angles map to congruent angles, parallelism is preserved, and orientation of the figure remains unchanged.
- Rule in coordinate geometry: A point (x, y) translated by (a, b) becomes (x + a, y + b).
- Example: Translate the point (3, –4) by (–2, 5). The result is (1, 1).
- Real-life examples: