Geometry Honors Day 2: Reflections 1/24/2013

Overview 1/24/2013 Warm-Up Review Translations Transformations Homework check Remaining questions Transformations Reflections Conclusion

Warm-Up 1/24/2013

Homework Check Right 2, down 1: U Left 2, Up 3, Vector Form: < -2, 3>, Rule: <x,y>  < x-2, y+3> Left 3, Up 4, Image: P <4, -4> <x,y>  <x+5, y-3> <x,y> <x-4, y+4>

Essential Questions What is a reflection? How do you reflect an image in a line? How do you describe a reflections in the coordinate plane in algebraic terms?

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).

Definitions Every reflection has a “black line/central line/mirror line” Line of symmetry: the line the preimage is reflected over. Reflection: is a transformation in which the preimage is flipped across the line of symmetry. Does a reflection have the property of isometry? Isometry: is when the preimage and the image are congruent! YES!!!

Take a piece of paper and cut it in half (hamburger style) Draw and label a shape and a line on ½ of the paper. – (may want figure towards the center of paper) Draw a point on the line to use as a reference point. Place the other ½ paper on top of the original, and trace the figure, the line and the point (be as exact as possible) Flip Sheet 2 over, and put it under the original. Align the lines of reflection and the reference points. Trace the image from Sheet 2 onto the original sheet. Label the original figure and the reflected figure. Make sure to try this on your own first! May want to walk students through this activity. HQ: what do you notice about the picture once the activity is complete.

Generalizing Reflections on the Coordinate Plan Review of Graphing: In your groups graph the following lines: y = x y = -x y = 3 x = -2 One student will need to graph the following on the board! May need to remind students what the coordinate plan is.

Developing Rule for Reflections Rule for: y – axis: x – axis: Line y = x Line y = -x Give students graph paper (cut into 4ths) each student needs 4 pieces. Have students draw a coordinate plan on the paper. And place an ordered pair in Quadrant 1. cannot have same x and y values!!! Fold the paper across the y-axis. (the ordered pair should be on the “back of the paper now”) Through the paper draw the ordered pair. label the coordinates of the new ordered pair that is in Quadrant 2. Create a rule for reflection across the y-axis. Fold the paper across the x-axis. (the ordered pair should be on the “back of the paper now”) Through the paper draw the ordered pair. label the coordinates of the new ordered pair that is in Quadrant 4. Create a rule for reflection across the x-axis. Fold the paper across the line y=x. (the ordered pair should be on the “back of the paper now”) Through the paper draw the ordered pair. label the coordinates of the new ordered pair. Create a rule for reflection across the line y=x. Fold the paper across the line y = -x . (the ordered pair should be on the “back of the paper now”) Through the paper draw the ordered pair. label the coordinates of the new ordered pair. Create a rule for reflection across the line y = -x.

Compositions A composition of transformations is the result of applying one transformation to a figure and then applying a second transformation to its image.

Example1: Find the image of A(3, 4) after a translation (x, y)  (x+2, y-3) followed by a translation (x, y)  (x-4, y-2). Write a rule for the single transformation that produces A’’.

Example 2: Find the image A(3, 4) after a glide described by the vector 0, 2 and a reflection in the line x = 1. Would the result be the same if you reflected A first, then translated it?

Glide reflection The composition of a glide (translation) and a reflection in a line parallel to the glide vector. You can tell an image is a glide reflection if the two pictures are  and have opposite orientations but not a line of symmetry.

Example 3: Each figure is an isometry of the figure at the left Example 3: Each figure is an isometry of the figure at the left. Tell whether their orientations are the same or opposite. Then classify the isometry.

Conclusion 1/24/2013 Write one thing you learned and one thing you still have questions about from today’s lesson. Should be written in the notes section of your notebooks!

Practice Page636 #1-17 **Adjust based on time**

Homework Reflection worksheet Composition worksheet