1-7 Transformations in the Coordinate Plane
Objectives: 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 or specify a sequence of transformations that will carry a
given figure onto another.
For the board: You will be able to identify reflections, rotations, and translations and graph
transformations in the coordinate plane.
Bell Work:
1. Find the values of x and y if (3, -2) = (x + 1, y – 3).
2. Find the values of x and y if (-8, 12) = (-2y, 4x).
Anticipatory Set:
A transformation is a change in the position, size, or shape of a figure.
The original figure is called the preimage. The resulting figure is called the image.
A transformation maps the preimage to the image.
Arrow (→) notation is used to describe a transformation, and primes (‘) are used to label the image.
Transformation
Description
Definition
Reflection
Flip
A transformation across a
line, called the line of
reflection.
Rotation
Turn
A transformation about a
point P, called the center of
rotation.
Picture
Arrow Notation
A
A’
C
B
B’
C’
C
B’
B
C’
D
slide
A transformation in which all
the points of a figure move
the same distance in the
same direction.
Dilation
Enlargement
or Reduction
D’
B’
C’
B
A
ABCD→A’B’C’D’
A’
A
Translation
ΔABC→ΔA’B’C’
A’
ΔABCD→A’B’C’D’
D’
C
D
A’
A transformation in which the
sides of a figure change in
size by a given factor.
A
C
C’
B’
B
ΔABC→ΔA’B’C’
Open the book to page 50 – 51 and read examples 1.
Examples: Identify the transformation and then use arrow notation to describe the transformation.
A.
B.
B
C
C’
A
B’
D
E
G
G’
F
F’
D’
E’
A’
rotation, ΔABC → ΔA’B’C’
reflection, DEFG → D’E’F’G’
Graphing Activity:
Practice: Identify the transformation and then use arrow notation to describe the tansformation.
A.
B’
C’
B
C
A’
A
dilation, ΔABC → ΔA’B’C’
B.
G’
F’
G
F D’
E’
D
E
translation, DEFG → D’E’F’G’
Open the book to page 51 and read example 2.
Example: A figure has vertices at A(1, -1), B(2, 3), and C(4, -2).
After a transformation, the image of the figure
has vertices at A’(-1, -1), B’(-2, 3), and C’(-4, -2).
Draw the preimage and image. then identify
the transformation and use arrow notation to
describe the transformation.
reflection
ΔABC → ΔA’B’C’
White Board Activity:
Practice: A figure has vertices at E(2, 0), F(2, -1), G(5, -1), and
H(5, 0). After a transformation, the image of the
figure has vertices at E’(0, 2), F’(1, 2), G’(1, 5), and
H’(0, 5). Draw the preimage and image. Then
identify the transformation.
Rotation
EFGH→E’F’G’H’
Assessment:
Question student pairs.
Independent Practice:
Text: pgs. 53 – 55 prob. 3 – 6, 8 – 10, 13 – 15.
For a Grade:
Text: pgs. 53 – 55 prob. 8, 10, 14.
B
B’
C’
A’ A
C
H’
G’
E’
F’
E
H
F
G