📚 Topic Summary
A translation in geometry is a transformation that slides a figure from one location to another without changing its size, shape, or orientation. Think of it as picking up a shape and placing it somewhere else on the coordinate plane without rotating or reflecting it. Translations are defined by a translation vector, which indicates the distance and direction of the slide. The notation for a translation is often represented as $T(x, y) = (x + a, y + b)$, where 'a' represents the horizontal shift and 'b' represents the vertical shift. Understanding the vocabulary and notation is key to solving translation problems!
🧠 Part A: Vocabulary
Match the term with its definition. Write the corresponding letter in the blank.
- _____ Translation
- _____ Pre-image
- _____ Image
- _____ Translation Vector
- _____ Coordinate Plane
A. The original figure before a transformation.
B. A transformation that slides a figure without changing its size or shape.
C. A plane with a horizontal x-axis and a vertical y-axis.
D. The figure after a transformation.
E. A vector that specifies the distance and direction of a translation.
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct words.
A translation is a ___________ that moves every point of a figure the same distance in the same ___________. The original figure is called the ___________, and the resulting figure is called the ___________. Translations are defined by a ___________. For example, $T(x, y) = (x + 3, y - 2)$ indicates a shift of 3 units to the ___________ and 2 units ___________.
Possible words: image, pre-image, vector, transformation, right, down, direction
🤔 Part C: Critical Thinking
Explain in your own words why translations are considered isometric transformations. What properties of the original figure are preserved during a translation?