5-7
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5-7. Transformations. Warm Up. Problem of the Day. Lesson Presentation. Pre-Algebra. 5-7. Transformations. Pre-Algebra. 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. - PowerPoint PPT PresentationTRANSCRIPT
Pre-Algebra
5-7 Transformations
5-7 Transformations
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
5-7 Transformations
Warm Up
Pre-Algebra
5-7 Transformations
Determine if the following sets of points form a parallelogram.
1. (–3, 0), (1, 4), (6, 0), (2, –4)
2. (1, 2), (–2, 2), (–2, 1), (1, –2)
3. (2, 3), (–3, 1), (1, –4), (6, –2)
yes
no
yes
Pre-Algebra
5-7 Transformations
Problem of the DayHow 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
transformation
translation
rotation
center of rotation
reflection
image
Vocabulary
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.
A. B.
reflection rotation
Pre-Algebra
5-7 Transformations
Additional Example 1C & 1D: Identifying Transformations
Identify each as a translation, rotation, reflection, or none of these.
C. D.
none of the these translation
Pre-Algebra
5-7 Transformations
Try This: Example 1A & 1B
Identify each as a translation, rotation, reflection, or none of these.
A
B C
A. B. A B
CD
A’ B’
C’D’
translation reflection
A’
B’ C’
Pre-Algebra
5-7 Transformations
Identify each as a translation, rotation, reflection, or none of these.
BC
DE
F
C. D.
A
A’
B’C’
D’
F’
E’
rotation none of these
Try This: Example 1C & 1D
Pre-Algebra
5-7 Transformations
Additional Example 2A: Drawing Transformations
Draw the image of the triangle after the transformation.
A
B
C
A. Translation along AB so that A’ coincides with B
A’
B’
C’
Pre-Algebra
5-7 Transformations
Additional Example 2B: Drawing Transformations
Draw the image of the triangle after the transformation.
A
B
C
B. Reflection across BC.
A’
B’
C’
Pre-Algebra
5-7 Transformations
Draw the image of the triangle after the transformation.
A
B
C
C. 90° clockwise rotation around point B A’
B’
C’
Additional Example 2C: Drawing Transformations
Pre-Algebra
5-7 Transformations
Try This: Example 2A
Draw the image of the polygon after the transformation.
A
B C
D
E
F
A’
B’ C’
D’
E’
F’
A. Translation along DE so that E’ coincides with D
Pre-Algebra
5-7 Transformations
Try This: Example 2B
Draw the image of the polygon after the transformation.
A
BC
D
E
F
B. Reflection across CD.
A’
B’C’
D’
E’
F’
Pre-Algebra
5-7 Transformations
Draw the image of the polygon after the transformation.
A
BC
D
E
F
C’
A’
B’
D’
E’F’
C. 90° counterclockwise rotation around point C
Try This: Example 2C
Pre-Algebra
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)
x
y
–2
2
Pre-Algebra
5-7 Transformations
B. Translation 10 units left
Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation.
Try This: Example 3B
x
y
–2
2
Pre-Algebra
5-7 Transformations
C. Reflection across the x-axis
Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation.
Try This: Example 3C
x
y
–2
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
(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)
translation
reflection
Pre-Algebra
5-7 Transformations
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
(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)
none
rotation
Lesson Quiz: Part 2