Warm Up 11-12-15 Which of the following is NOT a rigid transformation (or isometry) of the image below: a. b. C. d.

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Presentation transcript:

Warm Up Which of the following is NOT a rigid transformation (or isometry) of the image below: a. b. C. d.

Announcements Quiz on Friday

Rotation Rotation: the spinning of a figure or point around one central point. Described by the amount of degrees the figure is spun. We call this the degree of the rotation.

Under a Rotation Therefore a rotation is a rigid transformation or an isometry

Functional Notation Functional notation A 90  rotation is described by:f(x,y) = (-y,x) A 180  rotation is described by:f(x,y) = (-x,-y) A 270  rotation is described by:F(x,y) = (y,-x)

A transformation is described by f(x,y) = (-y, x). 1. Is this a rotation of 90, 180, or 270 degrees? 2. Under this rotation, the image of (5,2) is _________.

EX. If A(3,-6)  A(-6,-3), what is the degree of rotation?

Dilations  angle measure is congruent  distance (or length) is not congruent  NOT RIGID→ NOT ISOMETRIES  Represented by the equations  (x,y) → (x’, y’) where x’ = kx and y’ = ky and k is constant  Two types –contractions and expansions  Fixed points-only at the origin

Contraction Reduce_the original figure proportionally Contractions-when 0< k<1

Find the image of the given point under the transformation described by f(x,y) = ((2/3)x, (2/3)y) (6,6) (-12, -3)

Expansion E nlarges the original figure proportionally Expansions-when k>1

Find the image of the given point under the transformation described by f(x,y) = ((2)x, (2)y) (6,6) (-8, -3)

Name the kind of transformation represented by each. 1. (x,y) → (5x, 5y) 2. (x,y) → ((1/4)x, (1/4)y)

Scale Factor

Homework Journal Pg. 286 and Pg. 310