9-1. Reflections Going Deeper Essential question: How do you draw the image of a figure under a reflection? EXPLORE. Drawing a Reflection Image

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1 Nae lass ate 9-1 Reflections Going eeper Essential question: How do you draw the iage of a figure under a reflection? One type of rigid otion is a reflection. reflection is a transforation that oves points by flipping the over a line called the line of reflection. The figure shows the reflection of quadrilateral across line l. Notice that the pre-iage and iage are irror iages of each other. l 1 G-O.1.4 EXPLORE rawing a Reflection Iage Follow the steps below to draw the reflection iage of each figure. l l Houghton Mifflin Harcourt Publishing opany Place a sheet of tracing paper over the figure. Use a straightedge to help you trace the figure and the line of reflection with its arrowheads. Flip the tracing paper over and ove it so that line l lies on top of itself. Trace the iage of the figure on the tracing paper. Press firly to ake an ipression on the page below. Lift the tracing paper and draw the iage of the figure. Label the vertices. REFLET 1a. Make a conjecture about the relationship of the line of reflection to any segent drawn between a pre-iage point and its iage point. 1b. Make a conjecture about the reflection iage of a point that lies on the line of reflection. hapter Lesson 1

2 2 G-O.1.5 EXMPLE onstructing a Reflection Iage Work directly on the figure below and follow the given steps to construct the iage of after a reflection across line. Start with point. onstruct a perpendicular to line that passes through point. Label the intersection of the perpendicular and line as point X. Place the point of your copass on point X and open the copass to the distance X. Make an arc to ark this distance on the perpendicular on the other side of line. X Label the point where the arc intersects the perpendicular as point. E Repeat the steps for the other vertices of. (Hint: It ay be helpful to extend line in order to construct perpendiculars fro points and.) REFLET 2a. Reflections have all the properties of rigid otions. For exaple, reflections preserve distance and angle easure. Explain how you could use a ruler and protractor to check this in your construction. 2b. What steps should you take to construct the iage of a point after a reflection across line if the point lies on line? X Houghton Mifflin Harcourt Publishing opany hapter Lesson 1

3 The table provides coordinate notation for reflections in a coordinate plane. Rules for Reflections in a oordinate Plane Reflection across the x-axis (x, y) (x, -y) Reflection across the y-axis (x, y) (-x, y) Reflection across the line y = x (x, y) (y, x) 3 G-O.1.2 EXMPLE rawing a Reflection in a oordinate Plane You are designing a logo for a bank. The left half of the logo is shown. You will coplete the logo by reflecting this figure across the y-axis. In the space below, sketch your prediction of what the copleted logo will look like. 5 y -5 0 x 5-5 Houghton Mifflin Harcourt Publishing opany In the table at right, list the vertices of the left half of the logo. Then use the rule for a reflection across the y-axis to write the vertices of the right half of the logo. Plot the vertices of the right half of the logo. Then connect the vertices to coplete the logo. opare the copleted logo to your prediction. REFLET 3a. Explain how your prediction copares to the copleted logo. Left Half (x, y) Right Half (-x, y) (0, 4) (0, 4) (-3, 2) (3, 2) (-2, 0) 3b. How can you use paper folding to check that you copleted the logo correctly? hapter Lesson 1

4 PRTIE Use tracing paper to help you draw the reflection iage of each figure across line. Label the vertices of the iage using prie notation Houghton Mifflin Harcourt Publishing opany hapter Lesson 1

5 Use a copass and straightedge to construct the reflection iage of each figure across line. Label the vertices of the iage using prie notation Give the iage of each point after a reflection across the given line. 9. (3, 1); x-axis 10. (-6, -3); y-axis 11. (0, -2); y = x Houghton Mifflin Harcourt Publishing opany 12. (-4, 3); y-axis 13. (5, 5); y = x 14. (-7, 0); x-axis 15. (-1, 5); y = x 16. (10, 6); x-axis 17. (8, 0); y-axis 18. Plot several points on a coordinate plane. Then find their iages after a reflection across the line y = -x. Use the results to develop a rule for reflection across the line y = -x. hapter Lesson 1

6 19. s the first step in designing a logo, you draw the figure shown in the first quadrant of the coordinate plane. Then you reflect the figure across the x-axis. You coplete the design by reflecting the original figure and its iage across the y-axis. raw the copleted design. 20. When point P is reflected across the y-axis, its iage lies in Quadrant IV. When point P is reflected across the line y = x, its position does not change. What can you say about the coordinates of point P? y x 5-5 Houghton Mifflin Harcourt Publishing opany hapter Lesson 1

7 Nae lass ate dditional Practice 9-1 = Houghton Mifflin Harcourt Publishing opany = hapter Lesson 1

8 Proble Solving = = = = = = Houghton Mifflin Harcourt Publishing opany hapter Lesson 1