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## Lesson 7.1 Rigid Motion in a Plane

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**Lesson 7.1Rigid Motion in a Plane**Today, we will learn to… > identify the 3 basic transformations > use transformations in real-life situations**Transformations**The original figure is called the ____________ and the new figure is called the ____________. preimage image**Transformations**Preimage: A , B , C , D Image: A’ , B’ , C’ , D’**R**R REFLECTION**R**R Rotation**R**R Translation**Isometries**preserve length, angle measures, parallel lines, & distances between points**Theorems 7.1, 7.2, & 7.4Reflections, translations, and**rotations are isometries.**1. Name and describe the transformation.**the y-axis reflection over A’B’C’ ABC **2. Name the coordinates of the vertices of the preimage and**image. (0,4) (-4,4) (4,4) (-4,0) (4,0)**3. Name and describe the transformation.**x = -1 reflection over HGFE ABCD **4. Is the transformation an isometry?**Explain. NO YES NO YES**5. The mapping is a reflection. Which side should have a**length of 7? Explain. WX = 7**6. Name the transformation.**Find x and y. Reflection x = 40 y = 4**7. Name the transformation.**Find x and y. Reflection x = 12 y = 4**8. Name the transformation.**Find a, b, c, and d. reflection a = 73 b = 53 15 c = 8 d =**9. Name the transformation.**Find p, q, and r. rotation p = 19 q = 3 r = 7.5**10. Name the transformation and**complete this statement GHI ____ LKP reflection**11. Name the transformation that maps the unshaded turtle**onto the shaded turtle reflection translation rotation**Lesson 7.2Reflections**Today, we will learn to… > identify and use reflections > identify relationships between reflections and line symmetry**Reflection**2 images required**What is the line of reflection?**1. Is this a reflection? YES x = -2**What is the line of reflection?**3. Is this a reflection? YES y = 1**What is the line of reflection?**4. Is this a reflection? YES y = x**What is the line of reflection?**5. Is this a reflection? YES y = - x**When can I use this in “Real Life?”**Finding a minimum distanceTelephone Cable - Pole PlacementTV cable (Converter Placement)Walking DistancesHelps you work smarter not harder**Finding a minimum distance6. A new telephone pole needs to**be placed near the road at point C so that the length of telephone cable (AC + CB) is a minimum distance. Two houses are at positions A and B. Where should you locate the telephone pole?**Finding a minimum distance**A B C 1) reflect A 2) connect A’ and B A’ 3) mark C**Line of Symmetry**1 image reflects onto itself**1**2 3 4 5 6 7 8 7. How many lines of symmetry does the figure have?**180˚**n m A = can be used to calculate the angle between the mirrors in a kaleidoscope n = the number of lines of symmetry**1**2 3 4 5 6 180˚ 8 = 7 8 22.5˚**180˚**9 = 20˚ http://kaleidoscopeheaven.org**180˚**4 10. Find the angle needed for the mirrors in this kaleidoscope. = 45˚**Project?**1) Identify a reflection in a flag 2) Identify a line of symmetry**Reflection**Line of Symmetry**Reflection**Line of Symmetry**Lesson 7.3Rotations**students need tracing paper Today, we will learn to… > identify and use rotations**Rotation**Direction of Rotation? Center of Rotation? Angle of Rotation?**60˚**60˚ Angle of Rotation? Clockwise rotation of 60° Center of Rotation?**40°**40° Counter-Clockwise rotation of 40°**Theorem 7.3A reflection followed by a reflection is a**rotation. If x˚ is the angle formed by the lines of reflection, then the angle of rotation is 2x°.**A’**2x˚ B’ x˚ B’’ A’’ A B**A’**A A’’ 1. What is the degree of the rotation? 70˚ 140˚