Translations: graph the image (Tutorial Only)

Learning Objectives Define a translation as a rigid motion that slides a figure on the coordinate plane. Interpret translation rules written in coordinate notation, (x, y) -> (x + a, y + b). Interpret translation rules written in vector notation, T_{<a, b>}. Accurately graph the image of a point, line segment, or polygon given a specific translation rule. Determine the coordinates of an image's vertices by applying a translation rule algebraically. Verify that a translation preserves the size and shape (congruence) of the original figure. Ever wondered how video game characters move smoothly across the screen or how animators create the illusion of motion? 🎮 It all starts with a simple 'slide'! This tutorial will guide you through translations, a fu...

TermDefinitionExample TransformationA function that changes the position, orientation, or size of a geometric figure. The main types are translations, rotations, reflections, and dilations.Sliding a triangle 3 units to the right is a transformation. TranslationA transformation that slides every point of a figure the same distance in the same direction. It is a type of rigid motion.Moving every point of a square 4 units up and 2 units left. Pre-imageThe original geometric figure before a transformation is applied.If we are translating triangle ABC, then triangle ABC is the pre-image. ImageThe new figure that results from applying a transformation to the pre-image. The vertices of the image are often denoted with a prime symbol (').After translating triangle ABC, the new figure is tria...

Coordinate Rule for Translation (x, y) \rightarrow (x + a, y + b) This rule describes how to find the coordinates of the image. For any point (x, y) in the pre-image, add 'a' to the x-coordinate and 'b' to the y-coordinate. A positive 'a' means a shift to the right, negative 'a' means left. A positive 'b' means a shift up, negative 'b' means down. Vector Notation for Translation T_{<a, b>}(P) = P' This is another way to represent a translation. T stands for translation, and the subscript <a, b> is the translation vector. It states that translating point P by the vector <a, b> results in the image point P'. This is equivalent to the coordinate rule: T_{<a, b>}(x, y) = (x + a, y + b)....