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Coordinate Reflections - 2

Coordinate Reflections - 2. Reflecting over the y = x and y = -x lines. Homework: Reflections on the Coordinate Plane WS 2. UPDATE: Reflection Notation . The line y=x. Where the x and y coordinates are equal: (1,1), (5,5), (-3, -3)…. (2, 2). (-1, -1). (-5, -5).

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Coordinate Reflections - 2

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  1. Coordinate Reflections - 2 Reflecting over the y = x and y = -x lines Homework: Reflections on the Coordinate Plane WS 2

  2. UPDATE: Reflection Notation

  3. The line y=x Where the x and y coordinates are equal: (1,1), (5,5), (-3, -3)… (2, 2) (-1, -1) (-5, -5)

  4. Reflect across y = x Notation: Rule: Swap x and y

  5. Name the coordinates of the original object: W’ I’ W W: (9, 8) I: (9, 3) N: (1, 1) N’ I Name the coordinates of the reflected object: N W’: (8, 9) A point ON the line of reflection is its own reflection I’: (3, 9) N’: (1, 1)

  6. C' B' D' A' A(1, 2)  A'(2, 1) B(3, 5)  B'(5, 3) C(4, –3)  C'(–3, 4) D(2, –5)  D'(–5, 2)

  7. The line y = -x Where the x and y coordinates are opposites: (1,-1), (-5,5), (3, -3)… (-2, 2) (4, -4)

  8. Reflect across y = -x Rule: Swap and change both signs

  9. Name the coordinates of the original object: A: (-4, 6) B: (-1, 6) C: (-1, 3) A’ Name the coordinates of the reflected object: C’ A’: (-6, 4) B’ B’: (-6, 1) C’: (-3, 1)

  10. Name the coordinates of the original object: A: (1,2) B: (1,5) C: (3,2) Name the coordinates of the reflected object: B’ A’ A’: (-2,-1) B’: (-5, -1) C’ C’: (-2, -3)

  11. Reflection Notation

  12. Rules of REFLECTION x-axis y-axis y = x y = -x

  13. Reflect the object below over the x-axis and then the y-axis: Name the coordinates of the original object: R Would it make a difference if we reflected over the y-axis first and then the x-axis? Try it! Then reflect about what you discovered. R: (-9, 9) P: (-8, 5) P D D: (-2, 4) U: (-9, 2) U Name the coordinates of the reflected object: U’ U’’ R’’: (9, -9) P’’: (8, -5) D’’ D’ P’’ D’’: (2, -4) P’ U’’: (9, -2) R’’ R’ How were the coordinates affected when the object was reflected over both the x-axis and y-axis?

  14. Think About It  How were the coordinates affected when the object was reflected over both the x-axis and y-axis? Would it make a difference if we reflected over the y-axis first and then the x-axis? Try it! Then reflect about what you discovered. Would the result of this double reflection be the same as a rotation of the original figure of 180°?

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