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˚