Translations: graph the image

Learning Objectives Define and identify a translation as a rigid motion. Describe a translation using coordinate notation (x,y) -> (x+a, y+b). Graph the image of a point after a given translation. Graph the image of a polygon after a given translation. Determine the translation rule given a pre-image and its image. Understand that translations preserve shape, size, and orientation, resulting in congruent figures. Have you ever slid a piece of furniture across a room without turning or flipping it? 🛋️ That's a translation in real life! In this lesson, you'll learn how to move geometric shapes on a coordinate plane without changing their size or orientation. We'll explore how to graph these 'slides' and describe them using mathematical rules, which...

TermDefinitionExample TranslationA transformation that 'slides' a figure from one position to another without turning it or flipping it. Every point of the figure moves the same distance in the same direction.Sliding a triangle 3 units to the right and 2 units up. Pre-imageThe original figure before a transformation is applied. It is usually denoted by capital letters (e.g., A, B, C).If you start with triangle ABC, then ABC is the pre-image. ImageThe new figure formed after a transformation has been applied to the pre-image. It is denoted with prime notation (e.g., A', B', C').After translating triangle ABC, the new triangle A'B'C' is the image. Translation VectorA directed line segment that describes the direction and distance of a translation. It...

Coordinate Rule for Translation $(x, y) \rightarrow (x+a, y+b)$ To translate a point $(x, y)$ by 'a' units horizontally and 'b' units vertically, add 'a' to the x-coordinate and 'b' to the y-coordinate. 'a' is positive for right, negative for left. 'b' is positive for up, negative for down. Translation Vector Notation $ \langle a, b \rangle $ A translation can be described by a vector $\langle a, b \rangle$, where 'a' represents the horizontal shift and 'b' represents the vertical shift. This vector is applied to each point $(x, y)$ as $(x+a, y+b)$.