INTRODUCTION TO TRANSFORMATIONS AND TRANSLATIONS Unit 7 – Day 1

Introduction – Matching Card Game  Each of you has been handed a card with a figure plotted on a coordinate plane.  Find your classmate who has the “matching” figure.  Once you find your “match”, sit together and write a quick description of how your figures have been changed. Be as descriptive as possible! WRITE YOUR DESCRIPTIONS ON A PIECE OF NOTEBOOK PAPER TO TURN IN!  Solid is original, dotted is the new image.  Once all matches have been found, a few will share a few.

Unit 1: Transformations Essential Questions: Why are only four types of transformations needed to describe the motion of a figure? How can coordinates be used to describe a sliding motion or translation?

Transformations Definition: A Transformation is a change in the position, size, or shape of a geometric figure.

Think About The Situation – Page 196 B and C only

Investigation In this lesson, you will learn how coordinates can be used to transform shapes. You will investigate coordinate representation of rigid transformations that provide a way to reposition figures in a plane without changing the shape or the size of the figures.

Translation Definition: A Translation (slide) is a transformation that moves points the same distance and in the same direction. A translation in the coordinate plane is described by a vector.

Preimage and Image The preimage is the original figure.  Denoted as A The image is the figure after a transformation.  Denoted as A’ or “A prime” (This is called Prime Notation)

Group Work A translation, or sliding motion, is determined by distance and direction. By looking carefully at a simple shape and its translated image, you can discover patterns relating the coordinates of the shape and the coordinates of its image. Work with your partner to complete the questions in 15 minutes Problem 2 and 3 in your textbook. Page 198 and 199

Question 2 v

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General Rule Compare the transformation rules you developed for Part d of Problem 2 and for Parts c and e of Problem 3. In pairs, write a general rule that tells how to take any point (x, y) and find its translated image if the preimage is moved horizontally h units and vertically k units. Compare your rule with other pairs and resolve any differences.

**General Rule for Translations** (x, y)  (x + h, y + k) Describes a translation of h horizontal units (+ Right, - Left) k vertical units (+ Up, - Down)

Example Write a description and rule for the following translation *Hint: the Translated Image is Always has the Prime notation

Vector Notation Vector notation is another way to write rules of translations. A vector is written as  h = left/right  k = up/down

Homework Complete the assigned worksheet on Translations