1.2: Transformations

1
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.
2
Rotation (turn)

• Need the center of rotation labeled
• Need the angle of rotation labeled

A
A
90o angle of rotation, clockwise.
Center of rotation
Unless specified, all rotations are done
COUNTERCLOCKWISE
3
The Rule

• The general rule for a rotation counterclockwise
  about the origin by 90 is
• (X,Y) gt (-Y, X)

http//www.mathwarehouse.com/transformations/rotat
ions-in-math.php
4
Rotate ABC 270 degrees counterclockwise
5
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.
6
(No Transcript)
7
(No Transcript)
8
Translation (slide)

• Slide all parts of the figure the same distance
  and direction (slide it)

A
A
9
Translation in coordinate plane

• If ?ABC with A(-1,-3), B(1,-1), C(-1,0), Find
  the coordinates of the image after the
  translation
• (x,y) (x-3,y4)

Subtract 3 from all xs
Add 4 to all the ys
10
Finding the new points
(x,y) gt (x-3,y4)

• ?ABC
• A (-1,-3)
• B (1,-1)
• C (-1,0)

• ?ABC
• A (-4,1)
• B (-2,3)
• C (-4,4)

11
Find the coordinates of
Under the translation of (x-1, y-3)
12
Write the translation for this picture (x,y)
( x , y )
(2,4)
(-5,1)
(2,1)
(-5,-2)
13
(No Transcript)
14
(No Transcript)
15
Notation for transformations
Write in what the notation means

16
The end