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NAME ______________________________________________ DATE 9-1 ____________ PERIOD _____ Practice Reflections Draw the image of each figure under a reflection in line ᐉ. 2. ᐉ ᐉ COORDINATE GEOMETRY Graph each figure and its image under the given reflection. 3. quadrilateral ABCD with vertices A(⫺3, 3), B(1, 4), C(4, 0), and D(⫺3, ⫺3) in the origin 4. 䉭FGH with vertices F(⫺3, ⫺1), G(0, 4), and H(3, ⫺1) in the line y ⫽ x y x O Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. y 5. rectangle QRST with vertices Q(⫺3, 2), R(⫺1, 4), S(2, 1), and T(0, ⫺1) in the x-axis 6. trapezoid HIJK with vertices H(⫺2, 5), I(2, 5), J(⫺4, ⫺1), and K(⫺4, 3) in the y-axis y O x O y x x O ROAD SIGNS Determine how many lines of symmetry each sign has. Then determine whether the sign has point symmetry. 7. Chapter 9 8. 9. 9 Glencoe Geometry Lesson 9-1 1. NAME ______________________________________________ DATE 9-1 ____________ PERIOD _____ Word Problem Practice Reflections 1. REFLECTIONS Vincent is making a star with a horizontal line of symmetry. Complete the star by drawing the reflected image of the figure over line m. Table 4. INTERIOR DESIGN Wilfred hired an interior designer to layout the furniture in his bedroom. The designer produced the plan shown in the figure. Unfortunately, Lamp Wilfred’s Desk window is located on the opposite wall Bed from the plan. Wilfred decides to just reflect the plan over the vertical line through the center of the room. Draw the reflected plan. Window m Bureau 2. LINES OF SYMMETRY Maria placed a paper cutout on a table and then left to get some glue. Her friend James flipped over the cutout without telling Maria. Still, when Maria came back it was impossible for her to be able to see that anything had been changed. Draw a line through the figure that represents the line over which James must have flipped the figure. y 3. SYMMETRY Martha made the figure shown. How many lines of symmetry does the figure have? 5 O 5 x 5. What are the vertices of the image of this triangle if it is reflected over the yaxis? 6. What are the vertices of the image of this triangle if it is reflected over the line y = x? Chapter 9 10 Glencoe Geometry Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. TRIANGLES For Exercises 5 and 6, use the following information. Casey drew this triangle on the coordinate plane. NAME ______________________________________________ DATE 9-1 ____________ PERIOD _____ Enrichment Reflections in the Coordinate Plane Study the diagram at the right. It shows how the triangle ABC is mapped onto triangle XYZ by the transformation (x, y) → (⫺x ⫹ 6, y). Notice that 䉭XYZ is the reflection image with respect to the vertical line with equation x ⫽ 3. (x, y) → (⫺x ⫹ 6, y) y Y B 1. Prove that the vertical line with equation x ⫽ 3 is the perpendicular bisector of the segment with endpoints (x, y) and (⫺x ⫹ 6, y). (Hint: Use the midpoint formula.) X O x Z C x⫽3 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 2. Every transformation of the form (x, y) → (⫺x ⫹ 2h, y) is a reflection with respect to the vertical line with equation x ⫽ h. What kind of transformation is (x, y) → ( x, ⫺y ⫹ 2 k)? Draw the transformation image for each figure and the given transformation. Is it a reflection transformation? If so, with respect to what line? 3. (x, y) → (⫺x ⫺ 4, y) 4. (x, y) → (x, ⫺y ⫹ 8) y O Chapter 9 y O x 11 x Glencoe Geometry Lesson 9-1 A