Defining a Translation
Defining a translation is a Grade 7 geometry concept in Big Ideas Math Advanced 2, Chapter 2: Transformations, where a translation is a rigid transformation that slides every point of a figure the same distance in the same direction without rotating or resizing. The original figure is the pre-image and the translated figure is the image, with corresponding vertices labeled using prime notation (A maps to A prime).
Key Concepts
Property A translation is a rigid transformation that "slides" a figure across a plane to a new location. Every single point of the original figure (the pre image) moves the exact same distance and in the exact same direction to create the new figure (the image). Because it is a rigid motion, the figure does not rotate, reflect, or change its size. Therefore, the pre image and image are perfectly congruent and face the exact same way (they preserve orientation).
Examples Macro View: Sliding a physical ruler across your desk without rotating it. Micro Detail (Naming): When triangle ABC slides to a new position, the new triangle is named A'B'C' (read as "A prime, B prime, C prime"). Point A matches with A', B with B', and C with C'. Micro Detail (Direction): If you draw a straight line from A to A' and another from B to B', those lines will be perfectly parallel and the exact same length.
Explanation While the property tells us the shape just "slides," here are the micro details to watch out for: 1. Pre image vs. Image: The original starting shape is called the "pre image" (usually standard letters like A, B, C). The final landing spot is the "image" (indicated by the prime marks like A', B', C'). 2. Congruence: Because it's a "rigid" motion, the pre image and image are exactly identical. If the side length of AB was 5 units, the side length of A'B' is strictly 5 units. No stretching allowed!
Common Questions
What is a translation in geometry?
A translation is a rigid transformation that slides a figure to a new location. Every point moves the same distance in the same direction, preserving the size, shape, and orientation of the figure.
What is the difference between pre-image and image in a translation?
The pre-image is the original figure before the transformation, using standard letters like A, B, C. The image is the figure after the translation, labeled with prime marks like A prime, B prime, C prime.
Does a translation change the size or shape of a figure?
No. A translation is a rigid motion, so the pre-image and image are congruent. Every side length and angle measure is preserved. The figure only changes position.
What textbook covers defining translations in Grade 7?
Big Ideas Math Advanced 2, Chapter 2: Transformations covers translations including the pre-image and image naming conventions.