Unit 1: Transformations Day 3: Rotations Standard

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Presentation transcript:

Unit 1: Transformations Day 3: Rotations Standard

Warm Up # 3 8.27.2014 Have out Homework Write Rules for the following (#1-3) 1) Reflection across the x-axis 2) Reflection across the line y = x 3) A Translation three units up and five units left 4) Describe the transformation (using words): (x,y)  (-x, y)

Essential Question #4 How can coordinates be used to describe rotations?

Reflection Definition: A Rotation is a transformation that turns or spins a figure about a fixed point, often the origin. *** All rotations are counterclockwise about the origin unless otherwise stated***

Counter Clockwise

Let’s explore Rotations Together! You need 4 small pieces of graph paper. Place a labeled coordinate plane on each sheet

General Rules for Rotations Rotation of 90° 180° 270° 360°

Group Work Rotations about the origin have similar algebraic rules as reflections. A rotation, or turning motion, is determined by a point called the center of the rotation and a directed angle of rotation. Complete the worksheets in pairs/groups. The goal is to develop a better understanding of rotation rules

Example 1 Write the rule and graph the image of a 90° rotation

Example 2 Given the preimage coordinates, what are the coordinates of the image after a 90⁰ clockwise rotation about the image. A (4, 7) B (-3, 2) C (5, -1)

Example 3 A) Identify the transformation that occurred. B) Write the rule for the transformation.

Discussion What do are three types of transformations have in common?

Definition: Isometry An isometry is a transformation in which the preimage and image are congruent What does it mean to be congruent? Two figures are congruent if they have the exact same size and shape (≅)

Assessment 3-2-1: Write down 3 things you learned this week, 2 things you have a question about, and 1 thing you found interesting. Homework: Page 7 in packet Standard: for questions 4 – 6 you do not have to graph the image, just identify the coordinates!