Warm Up Suppose triangle ABC has the coordinates A(-1,2), B(4,-3), and C(3,5). Find the coordinates of the image after a translation three units to the left and 2 units up. Write the vector to represent this transformation. 10 minutes End

Warm Up Suppose triangle ABC has the coordinates A(-1,2), B(4,-3), and C(3,5). Find the coordinates of the image after a translation three units to the left and 2 units up. Write the vector to represent this transformation. A’(-4,4), B’(1, -1), C’(0, 7) <-3, 2>

Reflections

Homework Check

Today’s Objectives Students will experiment with reflections using dynamic software. Students will develop algebraic rules to represent reflections in the coordinate plane.

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

Reflections Investigation 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.

Group Work Time Keeper: 15 minutes Resource Manager: Reflections Worksheet (1/member) Reader: Read problems out loud to group Spy Monitor: Check in with other groups if you are stuck Complete Problems 1 and 2 When finished, turn to the back and start problems 3 and 4

Problems 3 and 4 Time Keeper: Set 20 minutes Reader: Read problems out loud to group Spy Keeper: Check with other groups if you are stuck

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!

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