Translations: graph the image (Tutorial Only)

Learning Objectives Identify a translation as a slide of a figure on a coordinate plane. Determine the coordinates of an image after a given translation. Graph the image of a single point after a specified translation. Graph the image of a polygon (e.g., triangle, quadrilateral) after a given translation rule. Describe a translation using both coordinate notation and a verbal description. Distinguish between the pre-image and the image in a translation. Have you ever slid a book across a table or moved a chess piece? ♟️ That's a 'translation' in action! In this tutorial, you'll learn how to 'slide' shapes on a graph, called a translation, and accurately plot where they land. Understanding translations helps us describe movement and patterns in...

TermDefinitionExample TranslationA transformation that slides a figure from one position to another without turning, flipping, or changing its size or shape.Sliding a square 3 units to the right and 2 units up on a grid. Pre-imageThe original figure or point before a transformation is applied.If point A is at (1,2) before moving, A is the pre-image. ImageThe new figure or point after a transformation has been applied. It is often denoted with a prime symbol (e.g., A').If point A(1,2) is translated to A'(4,3), A' is the image. Coordinate PlaneA two-dimensional surface formed by two perpendicular number lines (the x-axis and y-axis) used to locate points.The grid system where you plot points like (3, -1). Ordered PairA pair of numbers (x, y) that gives the precise location of...

General Translation Rule $(x, y) \rightarrow (x+a, y+b)$ This rule describes how to find the new coordinates of any point (x, y) after a translation. 'a' represents the horizontal shift (positive for right, negative for left), and 'b' represents the vertical shift (positive for up, negative for down). Horizontal Translation $(x, y) \rightarrow (x+a, y)$ Use this rule when a figure is only translated horizontally (left or right). The y-coordinate remains unchanged. Add 'a' for a shift to the right, subtract 'a' for a shift to the left. Vertical Translation $(x, y) \rightarrow (x, y+b)$ Use this rule when a figure is only translated vertically (up or down). The x-coordinate remains unchanged. Add 'b' for a shift upwards...