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

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Presentation transcript:

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

Translations, Reflections, Rotations RANS ORMATIONS Translations, Reflections, Rotations

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’

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

HOW TO PERFORM A 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) x y A (-8, 6) B (-3, 6) D (-3, 3) C (-8, 3) A’ (2, 6) B’ (7, 6) C’ (2, 3) D’ (7, 3)

HOW TO PERFORM A 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) x y A (-8, 6) B (-3, 6) D (-3, 3) C (-8, 3)

HOW TO PERFORM A 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)

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

HOW TO PERFORM A REFLECTION x y B’ (-7, 9) B (7, 9) A (3, 6) C (9, 2) 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) A‘ (-3, 6) C’ (-9, 2)

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

HOW TO PERFORM A REFLECTION x y B (7, 9) A (3, 6) C (9, 2) 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) A’ (3, -6) C’ (9, -2) B’ (7, -9)

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

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

HOW TO PERFORM A 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) x y A (8, 9) B (3, 3) C (8, 3)

HOW TO PERFORM A ROTATION

HOW TO PERFORM A 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) x y A (-8, 9) B (-3, 3) C (-8, 3) C’ (3, 8) A’ (9, 8) B’ (3, 3)