Unit 1 – Day 2 Reflections

Warm Up #2 (1.24.2014) 1. Suppose a translation slides the point X(-3, 4) to the point X’(-1, 1). Write a rule (x, y)  ( ___ , ___ ) that describes this translation. 2. The points A(2, 7) and B(-5, 4) are translated by the vector <-4, 1>. Determine the coordinates of the image points A’ and B’ Have Homework and Signed Syllabus out!!!

Unit 1: Transformations Essential Questions 1.24.2014 Why are only four types of transformations needed to describe the motion of a figure?   How can coordinates be used to describe a flip or reflection?

Reflection Notes: Intro Draw a picture of what you think a reflection looks like. Some things to think about: When/Where can you see a reflection? What does your reflection look like?

Do we see a reflection? What is that black line at sea level? What do you notice about the mountain and its reflection? What about the points on the black line? Are they reflected anywhere? Want students to see that every point of the actual mountain(preimage) is exactly the same distance from the black line as its corresponding point in the reflected mountain(image).

Reflection Definition: A Reflection is a transformation in which the preimage is flipped across a line of symmetry.

Line of Symmetry The Line of Symmetry is the line that the preimage is reflected over. When you connect the preimage and image with a line segment, the Line of Symmetry will be the Perpendicular Bisector of the segment

Group Work Just like with translations, line reflections can be expressed using coordinates. In this investigation, you will build coordinate models for reflections across vertical and horizontal lines, as well as across the lines y = x and y = -x. Time: 15 minutes Problem 8 and 9 Worksheet Page 202 in book When finished, get 10 and 11 Worksheet.

Questions 10 and 11 Time Keeper: Set 20 minutes Page 203

General Rules for Line Reflections Reflection across The x-axis: The y-axis: The line y = x: The line y = -x

Example Write the rule and graph the image

Reflection over other lines Remember! You can reflect across ANY line by thinking about the perpendicular bisector!

What if I can’t remember the rules? Take a piece of graph paper. Place a coordinate like (1,2) in quadrant 1. Fold the graph paper along your line of reflection. The new point will provide you with your rule for the 4 rules we have.

Assessment Class Discussion: What are some real-world examples of reflections? How do they relate to what we learned today? Homework: Worksheet