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Videos & Songs!

Learn about the different types of transformations in geometry including translation, reflections, and rotations. This video demonstrates how to perform each transformation and provides step-by-step instructions. Improve your geometry skills today!

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Videos & Songs!

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  1. Videos & Songs! • https://www.youtube.com/watch?v=0Z1aUhGCZs0 - Colin Dodds song • https://www.youtube.com/watch?v=NKtJd1hkI9k - transformation style

  2. T F RANS ORMATIONS Translations, Reflections, Rotations

  3. TRANSFORMATION Movement of a geometric figure • The result of a transformation is called the prime (’) • Blue figure is “Optimus” • Transformation of “Optimus” is red figure, called “OPTIMUS PRIME”! • Written as Optimus’

  4. TRANSLATION (Slide) - formed by moving every point on a figure the same distance in the same direction

  5. y A (-8, 6) B (-3, 6) A’ (2, 6) B’ (7, 6) C (-8, 3) D (-3, 3) C’ (2, 3) D’ (7, 3) x HOW TO PERFORMA TRANSLATION Move the figure 10 units right. A (-8, 6) (-8 + 10, 6)  A’ (2, 6) B (-3, 6) (-3 + 10, 6)  B’ (7, 6) C (-8, 3) (-8 + 10, 3)  C’ (2, 3) D(-3, 3) (-3 + 10, 3)  D’ (7, 3)

  6. y A (-8, 6) B (-3, 6) C (-8, 3) D (-3, 3) x HOW TO PERFORMA TRANSLATION To move a units right: • Take each point on the figure, and slide it a units to the right • Algebraically: Add a to the x-coordinate of each point. (x, y)  (x + a, y)

  7. HOW TO PERFORMA TRANSLATION • To move b units left: Subtract b from the x-coordinate of each point. (x, y)  (x - b, y) • To move c units up: Add c to the y-coordinate of each point. (x, y)  (x, y + c) • To move d units down: Subtract d from the y-coordinate of each point. (x, y)  (x, y - d)

  8. REFLECTIONS (Mirror Image/Flip) - a figure is flipped over a line called the line of reflection.

  9. B’ (-7, 9) y B (7, 9) A‘(-3, 6) A (3, 6) C (9, 2) C’ (-9, 2) x HOW TO PERFORMA REFLECTION Reflect the figure over the y-axis A (3, 6) A’(-3, 6) B (7, 9)  B’(-7, 9) C (9, 2)  C’(-9, 2)

  10. y x HOW TO PERFORMA REFLECTION To reflect over the y-axis: • Move each pointof the figure to the opposite side of the axis, the samedistancefrom the axis as the original point. • Algebraically: Multiply x-coordinate by -1 (x, y)  (-x, y) B (7, 9) A (3, 6) C (9, 2)

  11. y B (7, 9) A (3, 6) C (9, 2) C’ (9, -2) x A’ (3, -6) B’ (7, -9) HOW TO PERFORMA REFLECTION To reflect over the x-axis: Multiply y-coordinate by -1 (x, y)  (x, -y) A (3, 6) A’(3, -6) B (7, 9)  B’(7, -9) C (9, 2)  C’(9, -2)

  12. REMINDERS FOR REFLECTIONS • When reflecting over the y-axis, image is flipped horizontally. • Change the x-coordinate. • When reflecting over the x-axis, image is flipped vertically. • Change the y-coordinate

  13. ROTATIONS (Turn) – a figure is turned about a point.

  14. y x HOW TO PERFORMA ROTATION Rotate a figure 90°clockwise about the origin: • SWITCH the coordinates of each point (x, y) (y, x) • Then, MULTIPY the NEW second coordinate by -1 (y, x) (y, -1x) • In the end… (x, y)  (y, -1x) A (8, 9) B (3, 3) C (8, 3)

  15. HOW TO PERFORMA ROTATION

  16. A (-8, 9) y C’ (3, 8) A’ (9, 8) B (-3, 3) C (-8, 3) B’ (3, 3) x HOW TO PERFORMA ROTATION Rotate the figure 90°clockwise about the origin A (-8, 9) (9, -8)  A’ (9, 8) B (-3, 3)  (3, -3)  B’(3, 3) C (-8, 3)  (3, -8)  C’ (3, 8)

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