Transcript 1.2: Transformations

1.2: Transformations
CCSS
G-CO.2 Represent transformations in the plane using, e.g., transparencies and geometry
software; describe transformations as functions that take points in the plane as inputs and give
other points as outputs. Compare transformations that preserve distance and angle to those
that do not (e.g., translation versus horizontal stretch).
G-CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.
G-CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles,
perpendicular lines, parallel lines, and line segments.
G-CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed
figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of
transformations that will carry a given figure onto another.
G-CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the
effect of a given rigid motion on a given figure; given two figures, use the definition of
congruence in terms of rigid motions to decide if they are congruent.
Rotation (turn)
• Need the center of rotation labeled
• Need the angle of rotation labeled
A’
90o angle of
rotation,
clockwise.
A
Center of rotation
**Unless specified, all rotations are done COUNTERCLOCKWISE
The Rule
• The general rule for a
rotation
counterclockwise about
the origin by 90° is
(X,Y) => (-Y, X)
http://www.mathwarehouse.com/transformations/rotations-in-math.php
Rotate ABC 270 degrees
counterclockwise
1. RST
has vertices at R(0, 3), S(4, 0), and T(0, 0). Find the
coordinates of R after a 180º clockwise rotation about T.
2. FGH has vertices F(−1, 2), G(0, 0), and H(3, −1). Find the
coordinates of F after a 270° clockwise rotation about G.
Translation (slide)
• Slide all parts of the figure the same distance
and direction (slide it)
A
A’
Translation in coordinate plane
If ΔABC with A(-1,-3), B(1,-1), & C(-1,0), Find the
coordinates of the image after the translation:
(x,y)
(x-3,y+4)
Subtract 3 from all x’s
Add 4 to all the y’s
Finding the new points
(x,y)
ΔABC
A (-1,-3)
B (1,-1)
C (-1,0)
=>
(x-3,y+4)
ΔA’B’C’
A’ (-4,1)
B’ (-2,3)
C’ (-4,4)
Find the coordinates of
ABC 
Under the translation of
(x-1, y-3)
Write the translation for this picture
(x,y)
(x
,y
)
(2,4)
(-5,1)
(2,1)
(-5,-2)
Notation for transformations
Write in what the notation means
R90 
T( 2 , 3) 
rx axis 
ry  x 
T( 0 , 2 ) 
R270 
The end