4.4 Transformations with Matrices - PowerPoint PPT Presentation

1 / 24
About This Presentation
Title:

4.4 Transformations with Matrices

Description:

4.4 Transformations with Matrices 2. Reflections and Rotations 2) Reflections A reflection, or flip, is a transformation that creates symmetry. – PowerPoint PPT presentation

Number of Views:772
Avg rating:3.0/5.0
Slides: 25
Provided by: laur4209
Category:
Tags:
Transcript and Presenter's Notes

Title: 4.4 Transformations with Matrices

1
4.4 Transformations with Matrices
• 2. Reflections and Rotations

2
2) Reflections
• A reflection, or flip, is a transformation that
creates symmetry.
• You can use matrix multiplication to graph
reflections in the coordinate plane.
• There are four reflection matrices you are
responsible for knowing.

3
2) Reflections
• Reflection in the y-axis Reflection in the
x-axis

4
2) Reflections
• Reflection in the line y x Reflection in the
line y -x

5
2) Reflections
• Example 1  Given triangle ABC with A (4, 1), B
( 2, 5) and C (0, 2), reflect the triangle
across the y-axis. Then, sketch the image.

A B C
6
2) Reflections
• Example 1  Given triangle ABC with A (4, 1), B
( 2, 5) and C (0, 2), reflect the triangle
across the y-axis. Then, sketch the image.

A B C
y-axis reflection matrix
7
2) Reflections
• Example 1  Given triangle ABC with A (4, 1), B
( 2, 5) and C (0, 2), reflect the triangle
across the y-axis. Then, sketch the image.

A B C
A B C
y-axis reflection matrix
8
2) Reflections
9
2) Reflections
• Example 2 Given triangle ABC where A (4, 1), B
( 2, 5) and C (0, 2), reflect the triangle
across the x-axis. Then, sketch the image.

10
2) Reflections
• Example 2 Given triangle ABC where A (4, 1), B
( 2, 5) and C (0, 2), reflect the triangle
across the x-axis. Then, sketch the image.

A B C
11
2) Reflections
• Example 2 Given triangle ABC where A (4, 1), B
( 2, 5) and C (0, 2), reflect the triangle
across the x-axis. Then, sketch the image.

A B C
x-axis reflection matrix
12
2) Reflections
• Example 2 Given triangle ABC where A (4, 1), B
( 2, 5) and C (0, 2), reflect the triangle
across the x-axis. Then, sketch the image.

A B C
A B C
x-axis reflection matrix
13
2) Reflections

14
2) Rotations
• A rotation is a transformation that turns a
figure about a fixed point called a center of
rotation.
• You can rotate a figure as much as 360o.
• In this text, all rotations are counterclockwise
about the origin.

15
2) Rotations
• Rotation of 90o Rotation of 360o
• Rotation of 180o Rotation of 270o

16
2) Rotations
• Example 1  Given triangle ABC where A (4, 1), B
( 2, 5) and C (0, 2), rotate the triangle
270.  Then, sketch the image.

17
2) Rotations
• Example 1  Given triangle ABC where A (4, 1), B
( 2, 5) and C (0, 2), rotate the triangle
270.  Then, sketch the image.

A B C
18
2) Rotations
• Example 1  Given triangle ABC where A (4, 1), B
( 2, 5) and C (0, 2), rotate the triangle
270.  Then, sketch the image.

A B C
270o rotation matrtix
19
2) Rotations
• Example 1  Given triangle ABC where A (4, 1), B
( 2, 5) and C (0, 2), rotate the triangle
270.  Then, sketch the image.

A B C
A B C
270o rotation matrtix
20
2) Rotations
21
2) Rotations
• Example 2  The matrix below represents the
vertices of a polygon. Write a matrix to
represent the vertices after a rotation of 90o.

A B C D
22
2) Rotations
• Example 2  The matrix below represents the
vertices of a polygon. Write a matrix to
represent the vertices after a rotation of 90o.

A B C D
90o rotation matrtix
23
2) Rotations
• Example 2  The matrix below represents the
vertices of a polygon. Write a matrix to
represent the vertices after a rotation of 90o.

A B C D
A B C D
90o rotation matrtix
24
Homework
• Create some way to remember the 8 matrices used
for reflections and rotations.
• You are responsible for knowing all 8.
• The matrices are located on p.193 and p.194
• 2) p.196 10, 11, 13, 14, 18-21, 31, 32
• 3) QUIZ WEDNESDAY section 4.4
User Comments (0)
About PowerShow.com