📚 Topic Summary
In mathematics, a translation is a transformation that moves every point of a figure or a space by the same distance in a given direction. A translation can be described algebraically using the rule $(x, y) \rightarrow (x + a, y + b)$, where $a$ represents the horizontal shift and $b$ represents the vertical shift. If $a$ is positive, the figure moves to the right; if negative, it moves to the left. Similarly, if $b$ is positive, the figure moves up; if negative, it moves down.
Understanding this rule allows us to predict how a shape will move on a coordinate plane. This activity provides practice in applying these algebraic rules to various points and figures, enhancing your understanding of geometric transformations.
🔤 Part A: Vocabulary
Match the term with its definition:
- Term: Translation
- Term: Coordinate Plane
- Term: Transformation
- Term: Pre-image
- Term: Image
- Definition: A change in the position, size, or shape of a figure.
- Definition: The original figure before a transformation.
- Definition: A plane formed by the intersection of a horizontal number line (x-axis) and a vertical number line (y-axis).
- Definition: The figure after a transformation.
- Definition: A transformation that slides a figure without changing its size or shape.
✍️ Part B: Fill in the Blanks
A translation is a ________ that moves every point of a figure the same distance in the same ________. The algebraic rule for a translation is given by $(x, y) \rightarrow (x + a, y + b)$, where '$a$' represents the ________ shift and '$b$' represents the ________ shift. If '$a$' is ________, the figure moves to the right. If '$b$' is negative, the figure moves ________.
🤔 Part C: Critical Thinking
Explain how the translation rule $(x, y) \rightarrow (x - 3, y + 2)$ affects a triangle with vertices at (1, 1), (2, 3), and (4, 1). What are the new coordinates of the triangle's vertices after the translation?