Class Discussion. Line m is called a line of reflection and point O is called the midpoint. b. What relationship occurs between line m and segment

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1 Name: Geometry Pd. 1-3 Notes Date: Learning Goal: What is a reflection? How do you perform various reflections? Class Discussion As we prepare to work with reflections, we need to examine some relationships that occur between points and lines when a reflection occurs. Let s take a look at an example of a line reflection and discover some relationships. Line m is called a line of reflection and point O is called the midpoint. a. What relationships occur between the length of and? b. What relationship occurs between line m and segment c. Since line m is perpendicular to segment and goes through its midpoint, we call this line the. Reflection (over a line): A rigid motion in which each point in the pre-image has an image that is equidistant from the line of reflection, but is on the other side of the line of reflection A reflection in line m maps every point P onto P so that line m is the perpendicular bisector of Special case: If the point is ON the line of reflection, then the point remains ( or does not change locations) Notation:

2 Reflecting in Horizontal and Vertical Lines: Example 1: Graph ABC with vertices A(1, 3), B(5, 2), and C(2, 1) and its image after the reflection in the line n whose equation is Tip For Success: Always graph the line you are reflecting over first! Quick Write! Point A is units line n, so its reflection A is units line n. Points B is units line n, so its reflection is units line n. Points C is line n, so =. Example 2: Graph ABC with vertices A(1, 3), B(5, 2), and C(2, 1) and its image after the reflection in the line

3 1-4 Notes Learning Goal: What is a reflection? How do you perform various reflections over lines and points? What is a line of symmetry? Reflecting in the line Reflecting in the line 1) State the coordinates for each: 2) Do you notice anything happening between coordinates of the pre-image compared to the image? Do you notice anything happening between coordinates of the pre-image compared to the image? 3) Notation Pre-image: P(x,y) Image: P 4) Write the coordinates for the image of point (8,-3) under a Notation Pre-image: P(x,y) Image: P Write the coordinates for the image of point (8,-3) under a

4 Sample Description: Reflections and Congruency What is the relationship between and? Explain your answer!! Reflections across points Point Reflections: A reflection through a point so that the point P becomes the midpoint between the point A and its image A. Let s Try a Point Reflection! Geometry Leap Frog! Graph triangle ABC. A(1, 2), B(5, 5), C(5, 2) and reflect it through point (-1, 1). State the coordinates of the image A(1, 2) B(5, 5) C(5, 2)

5 Lines of Symmetry From past lessons: Can one side of the figure below be folded so that it matches the other? a. Sketch the line where we would fold the figure. This is called the. A figure has line symmetry when it can be folded onto itself Practice Directions: Complete each of the following problems. After you finish a page check your work using the key! 1. Complete the following sentence: The line of reflection (the y-axis) is also the of segment. 2. In the diagram below is graphed. State the coordinates of after r y = 2. SHOW ALL WORK!

6 Practice Part 1: Translation Practice Complete each of the following problems by the end of class: 1. Translate and label the image of RUST after a translation: T -3,-2 Draw and describe the vector the defines the translation. 2. a) Draw a vector showing the translation in the diagram below: b) Describe the transformation in words **Careful the axes are tricky! c) Write a rule in transformation notation for the translation of to 3. Graph and label with X(2,4), Y(6,0), and Z(7,2) and its image after the composite on T 0,-7 T -4,2. Show work. What is the relationship between the pre-image and the image? Justify your answer.

7 4. Determine the transformation rule that translates A(3,-2) to A (-1,4). Use appropriate transformation notation. 5. A translation maps the figure on the left to the figure on the right. What is the relationship between these two triangles? Using the relationship, solve for b and c. 6. In chess, the knight (the piece shaped like a horse) moves in an L pattern. The board shows two consecutive moves of a black knight during a game. Write a composition of translations for the moves. (Hint: Remember, order matters!) It may help to describe what happens first and what happens second. Now, rewrite the composition as a single translation that moves the night from its original position to its ending position.

8 Part 2: Reflection Practice 7. Graph ABC with vertices A(1, 3), B(5, 2), and C(2, 1) and its image after the reflection over the line y = x. For examples 8-10, choose a column to work on. The column on the right is meant to challenge you. Graph paper may be provided for scrap work. 8. What is the image of point A (15,3) under r Y=X? 8. What is the image of point A (15,3) under r y = 5? 9.What is the image of point B (-5,1) under r y=-x? 9. What is the image of point B (-5,1) under r y= -x What is the image of point C (2,-1) under a reflection across point M(0,2). 10. What is the image of point C (2,-1) under a reflection across point M(0,2). Determine the number of lines of symmetry for the figure: Hint Sketch them in