9.1, 9.2, & 9.3: Transformations -Translations, Reflections, & Rotations
VIDEO!
Write the following definitions:
-Transformation
-Rotation
-Translation
-Reflection
Transformations
Transformation: A change in a figure’s position, shape, or size.
Translations
Translation: a “slide” that moves a point a certain distance in a
certain direction
( x, y )  ( x  a , y  b )
Ex1) Find the image of the point
B(3, -4) after being translated left
5 and up 7.
Translations
Ex2) Given the transformation below, describe the translation.
X (2,1)  X ' (0,4)
Ex3) Write a rule to describe the
translation PQRS
P’Q’R’S’
Reflections
Reflection: a “flip” across a specified line
Some Reflection Rules:
**Original point and image are the
same distance away from the line
of reflection
Across x-axis: (x, y)  (-x, y)
Across y-axis: (x, y)  (x, -y)
Ex4) Find the image of L(-2, 5) after
being reflected across the y-axis.
Reflections
Ex6) Given the points R(-2,-1), A(1,-3), D(-2,-3), draw
ΔRAD and its reflection image across the line x = 2.
Rotations
Rotation: a “turn” of a certain angle about a point called the center
of rotation
*Unless stated otherwise, rotations are counterclockwise
Rotation Rules (around the origin):
90° (x, y)  (-y, x)
180° (x, y)  (-x, -y)
270° (x, y)  (y, -x)
Ex7) Find the image of P(-2,-2)
after being rotated 180° about the
origin.
Rotations
Ex8) Find the image of Z(1,-4) after
being rotated 270° about the
origin.
Ex9) Given the points X(0,-1), Y(1,2),
Z(4,1), draw ΔXYZ and its rotation of
90° about the origin.
Transformations
Ex 10) Use P(-5,3) as the preimage for each of the following
transformations:
Q) Translation:
10
( x, y )  ( x  4, y  1)
8
6
4
P
R) Reflection over:
2
-10 -8 -6 -4 -2
2
4
6
8 10
y  2
-2
-4
-6
-8
-10
S) Rotation of 270°
 about the origin
Transformations
Ex11) Find the image of point X(-1, 5) after being translated 4
to the right, reflected across y-axis, and then rotated 180°
about the origin.
Transformations
Ex12) What type of transformation is represented by each
figure?
b)
c)
a)
ON GRAPH PAPER!!!
Homework #26:
p.473 #9-14, 22
p.480 #1-13 odd
p.487 #31, 34 (about the origin ONLY)