Lesson 9 Reflections Learning Targets :

Transcription

1 Reflections Learning Targets : I can construct the line of reflection using the compass and a straightedge I can draw the reflected figure using a compass and a straightedge and on coordinate grid Opening Activity (Discussion) ABC is reflected across DE and maps onto A B C. Use your compass and straightedge to construct the perpendicular bisector of the segment connecting A to A. What do you notice about the perpendicular bisector? Example 2 a) Using the diagram below, construct the line of reflection for quadrilaterals ABCD and A B C D. Label the line of reflection XY. (Hint: Draw BB first)

2 In Conclusion So, we just learned that the line of reflection is the of the segment connecting a point on the pre-image and the corresponding point on the image. We also learned that the distance between a point on the pre-image and the line of reflection is to the distance between a point on the image and the line of reflection. In other words, a point on the pre-image and its corresponding point on the image are from the line of reflection. Notation: r l r l (P) = Q Reflecting on the coordinate grid Reflections Over the x- and y-axes Example 3. Reflect the figure with the given vertices across the given line. J(1,2) I(2,8) M(8,4); x-axis and y-axis a. State the coordinates of J I M, the image of JIM after r x-axis. J': I': M': b. State the coordinates of J I M, the image of JIM after r y-axis. J : I : M :

3 Reflections Over Other Horizontal and Vertical Lines x = : line y = : line Example 4 Draw JEN. J( 3,1) E( 6, 2) N( 5,6) a. State the coordinates of J E N, the of the image of JEN after r x=2. J': E': N': b. State the coordinates of J E N, the of the image of JEN after r y= 2. J : E : N :

4 Reflections Over a line y = x Example 3. Reflect ABC with the given vertices across the given line. A(5,2) B(10,4) C(0,10); y = x A': B': C': A reflection is a rigid transformation (isometry) that maps every point P in the plane to point P', across a line of reflection, m, such that: Case 1: if point P is ON line m, the point is its own reflection (P = P') and (point P is "fixed"). P m Case 2: if point P is NOT on line m, then m is the perpendicular bisector of P where m Properties preserved under a line reflection from the pre-image to the image. 1. distance (lengths of segments remain the same) 2. angle measures (remain the same) 3. parallelism (parallel lines remain parallel) 4. collinearity (points remain on the same lines) The orientation (lettering around the outside of the figure), is not preserved. The order of the lettering in a reflection is reversed (from clockwise to counterclockwise or vice versa).

5 Reflections Classwork 1. Construct the line of reflection for each pair of images below. 2. For numbers 1-6 find the coordinates of each image. 1. r x-axis (A) 2. r y-axis (B) 3. r y = x (C) 4. r x = 2 (D) 5. r y= -1 (E) 6. r x = -3 (F)

6 3. Given points A(3, 3), B(5, -2), and C(4, 4), graph ΔABC and its reflection image as indicated. a. ry-axis (ΔABC) b. rx-axis (ΔABC) 4. Quadrilateral ABCD is graphed in the coordinate plane with the vertices A(3,2), B(4,0), C(7, 2), and D(6,5) as shown in the figure. Part A: Quadrilateral ABCD will be reflected across the line x = 2 to form quadrilateral A B C D. List all quadrants of the xy-coordinate plane that will contain at least one vertex of quadrilateral A B C D. Part B: Quadrilateral ABCD will be reflected across the line x = 2 to form quadrilateral A B C D. What are the coordinates of C? Draw the line of reflection you can use to map one figure onto the other.

7 Reflections Homework 1. For problems a f find the coordinates of each image. a) r x-axis (A) b) r y-axis (B) c) r y = x (C) d) r x = 3 (D) e) r y= 2 (E) f) r x = -1 (F)

8 3. Given points D(-2, 1), E(1, 3), and F(2, -2), graph ΔDEF and its reflection image as indicated. a. ry-axis (ΔDEF) b. rx-axis (ΔDEF) c. rx = 2(ΔDEF) d. ry = 1(ΔDEF)