8-5 Translations, Reflections, and Rotations
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
8-5 Translations, Reflections, and Rotations
Warm Up
1. Subtract 3 from the x-coordinate and 2 from
the y-coordinate in (7, –4). (4, –6)
2. Multiply each coordinate by 3 in (4, 9). (12, 27)
3. Subtract 4 from the x-coordinate and add 3
to the to the y-coordinate in (–2, –1). (–6, 2)
8-5 Translations, Reflections, and Rotations
Problem of the Day
Some numbers appear as different
numbers when rotated or reflected. Name
as many as you can.
Possible answers: 6 and 9; 6999
and 6669; IV and VI; IX and XI
8-5 Translations, Reflections, and Rotations
Sunshine State Standards
MA.7.G.4.2 Predict the results of
transformations and draw transformed
figures, with and without the coordinate
plane.
Also MA.7.G.4.3
8-5 Translations, Reflections, and Rotations
Vocabulary
transformation
image
preimage
translation
reflection
line of reflection
rotation
8-5 Translations, Reflections, and Rotations
In mathematics, a transformation
changes the position or orientation of a
figure. The resulting figure is the image
of the original figure, called the preimage.
Images resulting from the transformations
described in the next slides are congruent
to the original figures.
8-5 Translations, Reflections, and Rotations
Types of Transformations
Translation
The figure slides along a straight line
without turning.
8-5 Translations, Reflections, and Rotations
Types of Transformations
Reflection
The figure flips across a line of
reflection, creating a mirror image.
8-5 Translations, Reflections, and Rotations
Types of Transformations
Rotation
The figure turns around a fixed point.
8-5 Translations, Reflections, and Rotations
Additional Example 1: Identifying Types of
Transformations
Identify each type of transformation.
A.
B.
The figure flips across
the y-axis.
The figure slides along
a straight line.
It is a reflection.
It is a translation.
8-5 Translations, Reflections, and Rotations
Check It Out: Example 1
Identify the type of transformation.
translation
8-5 Translations, Reflections, and Rotations
Additional Example 2: Graphing Transformations on
a Coordinate Plane
Graph the translation of quadrilateral ABCD
4 units left and 2 units down.
Each vertex is moved 4 units left and 2 units down.
8-5 Translations, Reflections, and Rotations
Additional Example 2 Continued
Write the coordinate of the vertices of the
image.
Quadrilateral ABCD
A(1, 3)
(x – 4, y – 2)
(1 – 4, 3 – 2)
A’B’C’D’
A’(–3, 1)
B(4, 4)
C(4, 1)
(4 – 4, 4 – 2)
(4 – 4, 1 – 2)
B’(0, 2)
C’(0, –1)
D(1, –1)
(1 – 4, –1 – 2)
D’(–3, –3)
The coordinates of the vertices of quadrilateral A'B'C'D'
are A'(–3, 1), B'(0, 2), C'(0, –1), and D'(–3, –3).
8-5 Translations, Reflections, and Rotations
Reading Math
A’ is read “A prime” and is used to represent
the point on the image that corresponds to
point A of the original figure
8-5 Translations, Reflections, and Rotations
Check It Out: Example 2
Graph the translation of quadrilateral ABCD 5
units left and 3 units down.
y
B
A
4
B’
A’
–4
D’
2
C
D
–2
–2
C’
–4
2
4
x
8-5 Translations, Reflections, and Rotations
Additional Example 3: Graphing Reflections on a
Coordinate Plane
Graph the reflection of the figure across the
indicated axis. Write the coordinates of the
vertices of the image.
8-5 Translations, Reflections, and Rotations
Additional Example 3 Continued
A. x-axis
The x-coordinates of the
corresponding vertices are the
same, and the y-coordinates of
the corresponding vertices are
opposites.
The coordinates of the
vertices of triangle A’D’C’
are A’(–3, –1), D’(0, 0),
and C’(2, –2).
8-5 Translations, Reflections, and Rotations
Additional Example 3 Continued
B. y-axis
The y-coordinates of the
corresponding vertices are the
same, and the x-coordinates of
the corresponding vertices are
opposites.
The coordinates of the vertices
of triangle A’D’C’ are A’(3, 1),
D’(0, 0), and C’(–2, 2).
8-5 Translations, Reflections, and Rotations
Check It Out: Example 3
Graph the reflection of quadrilateral ABCD
across the x-axis.
8-5 Translations, Reflections, and Rotations
Additional Example 4: Graphing Rotations on a
Coordinate Plane
Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0).
Rotate ∆ABC 180° about the origin. Write the
coordinates of the vertices of the image.
y
B
3
Cx
A
C’
A’
–3
B’
The corresponding sides, AC
and AC’ make a 180° angle.
Notice that vertex C is 4 units
to the right of vertex A, and
vertex C’ is 4 units to the left
of vertex A.
The coordinates of the vertices
of triangle A’B’C’ are A’(0, 0),
B’(–2, –3), and C’(–4, 0).
8-5 Translations, Reflections, and Rotations
Check It Out: Example 4
Rotate the graph of quadrilateral ABCD 90°
clockwise about the origin.
8-5 Translations, Reflections, and Rotations
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
8-5 Translations, Reflections, and Rotations
Lesson Quiz
1. Identify the transformation. reflection
2. The figure formed by (–5, –6), (–1, –6), and
(3, 2) is translated 6 units right and 2 units up.
What are the coordinates of the new figure?
(1, –4), (5, –4), (9, 4)
3. Graph the triangle with vertices A(0, 0), B(–3, 0),
C(–1, 4). Reflect ∆ABC across the y-axis and give the
coordinates of the vertices of the image.
A'(0, 0), B'(3, 0), C'(1, 4)
8-5 Translations, Reflections, and Rotations
Lesson Quiz for Student Response Systems
1. Identify the transformation.
A. translation
B. reflection
C. rotation
D. none
8-5 Translations, Reflections, and Rotations
Lesson Quiz for Student Response Systems
2. The figure formed by (–3, 2), (–4, 1), and (–1, –5)
is translated 3 units right and 5 units up. What are the
coordinates of the new figure?
A. (–6, –3), (–7, –4), (–4, –10)
B. (0, 7), (–7, –4), (2, –10)
C. (0, 7), (–1, 6), (2, 0)
D. (–6, –3), (–1, 6), (–4, 0)