TRANSFORMATION. TRANSFORMATION Foldable PRIME Original New IN MATH TERMS…. P -> P’

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Presentation transcript:

TRANSFORMATION

Foldable

PRIME Original New IN MATH TERMS…. P -> P’

Matrix

On the back of your foldable Matrix-Scalar Multiplication – multiply each element of the matrix by a real number Given enlargement reduction Given a Picture A (1,1) B (1,4) C (6,1) A’ (2,2) B’ (2,8) C’ (12,2) A’’ (.5,.5) B’’ (.5,2) C’’ (3,.5) A B C X 1 1 6 Y 1 4 1 A B C 1 1 6 1 4 1 2 A’ B’ C’ 2 2 12 2 8 2 A B C 1 1 6 1 4 1 A’ B’ C’ .5 .5 3 .5 2 .5 = 1/2 =

REFLECTION Mirror line; any that is reflected across X-axis (x,y) -> (x,-y) A B C A’ B’ C’ x 2 4 4 x y 2 2 6 -y Y-axis (x,y) -> (-x,y) A B C A’ B’ C’ x 2 4 4 -x y 2 2 6 y Y=X (x,y) -> (y,x) A B C A’ B’ C’ x 2 4 4 x y 2 2 6 y Y=-x (x,y) -> (-y,-x) A B C A’ B’ C’ x 2 4 4 x y 2 2 6 y Y (2,4) B’ (6,4) C’ C (4,6) C (4,6) C’ (-4,6) C (4,6) C (4,6) (2,2) A’ A (2,2) B (4,2) B’ (-4,2) A’ (-2,2) A (2,2) B (4,2) B (4,2) X A (2,2) A (2,2) B (4,2) B’ (4,-2) A (-2,2) A’ (2,-2) C’ (4,-6) C’ (-6,4) (-2,4) B’ 2 4 4 -2 -2 -6 -2 -4 -4 2 2 6 2 2 6 2 4 4 -2 -2 -6 -2 -4 -4

ROTATION a point which a figure is turned-about during a rotation transformation 90⁰ (x,y) -> (-y,x) A B C A’ B’ C’ x 2 4 4 x y 2 2 6 y 180⁰ (x,y) -> (-x,-y) A B C A’ B’ C’ x 2 4 4 x y 2 2 6 y 270⁰ (x,y) -> (y,-x) A B C A’ B’ C’ x 2 4 4 x y 2 2 6 y 360o is same Y (-4,6) C’ (-4,2) B’ C (4,6) C (4,6) C (4,6) A (2,2) B (4,2) A (2,2) A (2,2) B (4,2) A’ (-2,2) X B (4,2) (-4,-2) B’ A’ (-2,-2) A(2,-2) C’ (-4,-6) C’ (6,-4) B’ (2,-4) -2 -2 -6 2 4 4 -2 -4 -4 -2 -2 -6 2 2 6 -2 -4 -4

COMPARE AND CONTRAST

Tessellation A collection of figures that cover a plane with no gaps or overlaps

x’ y’ (9,6) Translation x y Translate: (7, 3) Given: (x + 2, y + 3) A ----------------------- SLIDE x y Translate: (7, 3) Given: (x + 2, y + 3) x’ y’ (9,6)

What’s Missing?

symmetry Rotational Symmetry: the figure can be mapped onto itself by a rotation of 180° or less about the origin center of the figure Line of Symmetry: a figure that can be mapped onto itself by reflection in a line = 360/# of symmetrical lines 360 3 60, 120, 180 360 4 45, 90, 135, 180 180 360 1

Dilation

Given a figure; Prime is always on top Reduction - original size to small B’ A B A B A’ B’ x 2 4 x Y 2 2 y B 1 2 1 1 15 1/2 A 9 AB’ AB 15 9 5 3 Enlargement- original size to large A B A B A’ B’ x 2 4 x Y 2 2 y 4 8 4 4 2

Examples