Transcript Course 3 Chapter 5 Lesson 7

5-7
5-7 Transformations
Transformations
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
5-7 Transformations
Warm Up
Determine if the following sets of points form a
parallelogram.
1. (–3, 0), (1, 4), (6, 0), (2, –4)
yes
2. (1, 2), (–2, 2), (–2, 1), (1, –2) no
3. (2, 3), (–3, 1), (1, –4), (6, –2) yes
Pre-Algebra
5-7 Transformations
Problem of the Day
How can you move just one number to a different
triangle to make the sum of the numbers in each
triangle equal? (Hint: There do not have to be
exactly 3 numbers in each triangle.)
Move the 9 to the first triangle.
Pre-Algebra
5-7 Transformations
Learn to transform plane figures using
translations, rotations, and reflections.
Pre-Algebra
5-7 Transformations
Vocabulary
transformation
translation
rotation
center of rotation
reflection
image
Pre-Algebra
5-7 Transformations
When you are on an amusement park ride,
you are undergoing a transformation. Ferris wheels
and merry-go-rounds are rotations. Free fall rides
and water slides are translations. Translations,
rotations, and reflections are type of
transformations.
Pre-Algebra
5-7 Transformations
The resulting figure or image, of a translation,
rotation or reflection is congruent to the original
figure.
Pre-Algebra
5-7 Transformations
Additional Example 1A & 1B: Identifying
Transformations
Identify each as a translation, rotation,
reflection, or none of these.
B.
A.
reflection
Pre-Algebra
rotation
5-7 Transformations
Additional Example 1C & 1D: Identifying
Transformations
Identify each as a translation, rotation,
reflection, or none of these.
C.
none of the these
Pre-Algebra
D.
translation
5-7 Transformations
Try This: Example 1A & 1B
Identify each as a translation, rotation,
reflection, or none of these.
A.
B.
A’
A
C
B
C
C’
D
D’
B’
translation
Pre-Algebra
B
A
C’
A’
B’
reflection
5-7 Transformations
Try This: Example 1C & 1D
Identify each as a translation, rotation, reflection,
or none of these.
E’
C.
F’
A
F
E
Pre-Algebra
D’
B
C’ B’
C
D rotation
A’
D.
none of these
5-7 Transformations
Additional Example 2A: Drawing Transformations
Draw the image of the triangle after the
transformation.
A. Translation along AB so that
A’ coincides with B
A
B A’
B’
C
C’
Pre-Algebra
5-7 Transformations
Additional Example 2B: Drawing Transformations
Draw the image of the triangle after the
transformation.
B. Reflection across BC.
A
B
B’
C
C’
A’
Pre-Algebra
5-7 Transformations
Additional Example 2C: Drawing Transformations
Draw the image of the triangle after the
transformation.
C’
C. 90° clockwise
rotation around point B
A’
A
B’
B
C
Pre-Algebra
5-7 Transformations
Try This: Example 2A
Draw the image of the polygon after the
transformation.
A. Translation along DE so that B’
E’ coincides with D
F’
A’
B
C
A
E’
F
E
Pre-Algebra
D
C’
D’
5-7 Transformations
Try This: Example 2B
Draw the image of the polygon after the
transformation.
B. Reflection across CD.
B
A
Pre-Algebra
C C’
B’
F
D D’ F’
E
E’
A’
5-7 Transformations
Try This: Example 2C
Draw the image of the polygon after the
transformation.
C. 90° counterclockwise
rotation around point C
B
A
F
E
Pre-Algebra
C C’
B’
D
D’
F’
A’
E’
5-7 Transformations
Additional Example 3A: Graphing Transformations
Draw the image of a triangle with vertices of (1, 1),
(2, –2 ), and (5, 0) after each transformation.
A. 180° counterclockwise rotation around (0, 0)
Pre-Algebra
5-7 Transformations
Additional Example 3B: Graphing Transformations
Draw the image of a triangle with vertices of (1, 1),
(2, –2 ), and (5, 0) after each transformation.
B. Translation 5 units left
Pre-Algebra
5-7 Transformations
Additional Example 3C: Graphing Transformations
Draw the image of a triangle with vertices of (1, 1),
(2, –2 ), and (5, 0) after each transformation.
C. Reflection across the x-axis
Pre-Algebra
5-7 Transformations
Try This: Example 3A
Draw the image of a shape with vertices of (1, –2),
(3, 2), (7, 3), and (6, –1) after each transformation.
A. 180° clockwise rotation around (0, 0)
y
2
x
–2
Pre-Algebra
5-7 Transformations
Try This: Example 3B
Draw the image of a shape with vertices of (1, –2),
(3, 2), (7, 3), and (6, –1) after each transformation.
B. Translation 10 units left
y
2
x
–2
Pre-Algebra
5-7 Transformations
Try This: Example 3C
Draw the image of a shape with vertices of (1, –2),
(3, 2), (7, 3), and (6, –1) after each transformation.
C. Reflection across the x-axis
y
2
x
–2
Pre-Algebra
5-7 Transformations
Lesson Quiz: Part 1
Given the coordinates for the vertices of
each pair of quadrilaterals, determine
whether each pair represents a translation,
rotation, reflection, or none of these.
1. (2, 2), (4, 0), (3, 5), (6, 4)
and
translation
(3, –1), (5, –3), (4, 2), (7, 1)
2. (2, 3), (5, 5), (1, –2), (5, –4)
and
(–2, 3), (–5, 5), (–1, –2), (–5, –4)
Pre-Algebra
reflection
5-7 Transformations
Lesson Quiz: Part 2
Given the coordinates for the vertices of
each pair of quadrilaterals, determine
whether each pair represents a translation,
rotation, reflection, or none of these.
3. (1, 3), (–1, 2), (2, –3), (4, 0)
and
none
(1, –3), (–1, 2), (–2, 3), (–4, 0)
4. (4, 1), (1, 2), (4, 5), (1, 5)
and
(–4, –1), (–1, –2), (–4, –5), (–1, –5)
Pre-Algebra
rotation