Videos Songs https www youtube comwatch v0 Z

Videos & Songs! • https: //www. youtube. com/watch? v=0 Z 1 a. Uh. GCZs 0 - Colin Dodds song • https: //www. youtube. com/watch? v=NKt Jd 1 hk. I 9 k - transformation style

TRANS FORMATIONS 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. y 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) A (-8, 6) C (-8, 3) B (-3, 6) A’ (2, 6) B’ (7, 6) D (-3, 3) D’ (7, 3) C’ (2, 3) x

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

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

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) y B (7, 9) A (3, 6) C (9, 2) x

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

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, -1 x) – In the end… (x, y) (y, -1 x) y A (8, 9) B (3, 3) C (8, 3) x

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