Draw glide reflection images of figures2/12/2024 GEOMETRY LESSON 12-4 Compositions of Reflections Use the diagram for Exercises 1–3. Find the image of PQ for a glide reflection where the glide is 0,–8 and the reflection line is x = 0. It is a reflection of Z across a vertical line. So the figure on the right and Z have opposite orientations. The segment connecting the horizontal segments of the figure on the right slopes down from left to right. The segment connecting the horizontal segments of the letter Z slopes up from the left to the right. The orientation of the figure to the left of the dashed line is opposite the figure to the right of the dashed line. GEOMETRY LESSON 12-4 Compositions of Reflections Tell whether orientations are the same or opposite. GEOMETRY LESSON 12-4 Compositions of Reflections (continued) 12-4 The glide reflection image A B C has vertices A (6, 7), B (–4, 4), and C (2, 2). Then, reflect the translated image in the line x = 1. Find the image of ABC for a glide reflection where the glide is 0, 2 and the reflection line is x = 1. 12-4Ī B D C C’ B’ D’ A’ A glide reflection is a composition of a translation and a reflection in a line parallel to the translation vector.įirst, translate ABC by 0, 2. So the letter D is rotated 86° clockwise, or 274° counterclockwise, with the center of rotation at point A. The center of rotation is the point where the lines intersect, and the angle is twice the angle formed by the intersecting lines. Compositions of Reflections The composition of two reflections in intersecting lines is a rotation. GEOMETRY LESSON 12-4 The letter D is reflected in line x and then in line y. Find the image of the reflection through another reflection in line y. 12-4įind the image of D through a reflection in line x. The arrow shows the direction and distance of the translation. The final image is a translation of the original figure. Then, find the image of the first reflection in line m. GEOMETRY LESSON 12-4 Compositions of Reflections Find the image of the figure for a reflection in line and then in line m. The arrow is perpendicular to lines and m with length equal to twice the distance from to m. What is the most amount of reflections required to create an isometry? The Fundamental Theorem of Isometries: In a plane, one of two congruent figures can be mapped onto the other by AT MOST a composition of three reflections.įirst, find the reflection image in line. This suggests that one figure is a translation image of the other and not a rotation image. Corresponding sides of the figures appear to be parallel. The figures appear to be congruent, and their orientations are the same. GEOMETRY LESSON 12-4 Compositions of Reflections Judging by appearances, is one figure a translation image or rotation image of the other? Explain. The angle of rotation is equal to TWICE the measure of the angle of intersection. Rotation: A reflection across two intersecting lines. The length of translation is equal to TWICE the distance between the parallel line. Translation: A reflection across two parallel lines. 12-4ġ2.4 Composition of Functions Another way to define translations and rotations: A translation or rotation is a composition of reflections. GEOMETRY LESSON 12-4 Compositions of Reflections Solutions 7. GEOMETRY LESSON 12-4 Compositions of Reflections (For help, go to Lessons 12-1 and 12-2.) 12-4ġ. Draw images of the figure for a reflection in DG and for the translation vector FG. the x-axis 3.y = 1 Draw RST described above and its translation image for each translation vector. Given points R(–1, 1), S(–4, 3), and T(–2, 5), draw RST and its reflection image in each line.
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