3-2: Translations

translation

to vertically and/or horizontally shift a figure

k represents the ___________ ____________

vertical shift (up or down)

symbolic form

P(x, y) → P'(x + h, y + k)

h represents the ___________ ____________

horizontal shift (right or left)

Apply the translation rules on the preimage coordinates to find the coordinates of the image: Triangle CDE with vertices C(2, -1), D(7, -4), and E(4, -6): (x, y) → (x - 3, y + 8) C'( ____, ____) D'( ____, ____) E'( ____, ____)

C'(-1, 7) D'(4, 4) E'(1, 2) x - 3 : left 3 y + 8 : up 8

Apply the translation rules on the preimage coordinates to find the coordinates of the two images: Rectangle LMNP with vertices L(-2, 7), M(2, 3), N(0, 1), and P(-4, 5): (a) Translation: (x, y) → (x + 6, y -8) (b) Reflection: in the y-axis L'( ____, ____) M'( ____, ____) N'( ____, ____) P'( ____, ____)

L'(-4, -1) M'(-8, -5) N'(-6, -7) P'(-2, -3) x + 6 : right 6 y - 8 : down 8

Write a rule to describe each transformation: A(2, -1), B(1, 3), C(5, 3) A'(-1, -5), B(-2, -1), C'(2, -1)

P(x, y) → P' (x - 3, y - 4) *change in x coordinate: -3 *change in y coordinate: -4

Write a rule to describe each transformation: I(-5, 0), J(-5, 3), K(-1, 4), L(-4, 0) I'(-5, -2), J' (-5, 1), K'(-1, 2), L'(-4, -2)

P(x, y) → P' (x, y - 2) *change in x coordinate: +0 *change in y coordinate: -2

Write a rule to describe each transformation: E(-5, 0), F(-4, 5), G(-2, 5), H(-4, 0) E'(1, -2), F'(2, 3), G(4, 3), H(2, -2)

P(x, y) → P'(x + 6, y - 2) *change in x coordinate: +6 *change in y coordinate: -2

Apply the translation rules on the preimage coordinates to find the coordinates of the image: Rectangle QRST with vertices Q(-6, -1), R(-3, 1), S(1, -5), and T(-2, -7): (x, y) → (x + 5, y + 7) Q'( ____, ____) R'( ____, ____) S'( ____, ____) T'( ____, ____)

Q'(-1, 6) R'(2, 8) S'(6, 2) T'(3, 0) x + 5 : right 5 y + 7 : up 7

Apply the translation rules on the preimage coordinates to find the coordinates of the two images: Triangle XYZ with vertices X(-3, 7), Y(-2, 1), and Z(-5, 2): (a) Reflection: in the x-axis (b) Translation: (x, y) → (x + 9, y + 2) X'( ____, ____) Y'( ____, ____) Z'( ____, ____)

X'(6, -5) Y'(7, 1) Z'(4, 0) x + 9 : right 9 y + 2 : up 2