november 28, 2011

November 28, 20111) Graph your

Computation Challenge

2) Write your HW in your agenda: NONE

3) Complete the Warm-Up

4) I’m collecting Unit 2 and 3 Notes. Put your name on them:

- Concept Map

- KIM Chart

-Notes/organizers

WARM-UP:

Solve the following problems:

1. 3 + -4 7. -4 x 22. 4 – (-6) 8. 3 x -43. 2 – 9 9. -16 ÷ 44. -6 + 2 10. 3 ÷ -15. -7 – (-10) 11. -5 x -76. 8 + -4 12. -15 ÷ -5

November 29, 2011

1) Write your HW in your agenda: Practice 32 worksheet

2) Open your HWP to p. 100 and leave it on your desk.

3) Set up for Cornell Notes.

4) Answer the following question for your Warm-Up:

What is a transformation?

How are objects transformed?

GA Performance StandardsM7G1: Students will construct plane figures that meet given conditions.

a. Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

b. Recognize that many constructions are based on the creation of congruent triangles.   

M7G2: Students will demonstrate understanding of transformations.

a. Demonstrate understanding of translations, dilations, rotations, reflections, and relate symmetry to appropriate transformations.

b. Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation, rotation, or reflection.

Unit 4 Flip, Slide, and Turn

basic constructions

perpendicular lines

perform

bisect a line segment

copy a line segment

bisect an angle

parallel lines

copy an angle

understand

reflections

rotations translations

determine

coordinates

rotations

translations

reflections

In mathematics, a transformation changes the position or orientation of a figure. The resulting figure is the image of the original. Images resulting from the transformations are congruent to the original figure or the pre-image.

Course 2

8-10 Translations, Reflections, and Rotations

What do you notice about these objects?

What do we need to pay attention to when objects are

reflected?

Course 2

8-10 Transformations

What am I learning today?Transformations

What will I do to show that I learned it?

Determine coordinates resulting from a reflection.

Graph the reflection of the figure across the x-axis. Write the coordinates of the vertices of the image.

Graphing Reflections on a Coordinate Plane

Course 2

8-10 Reflections

PRE-IMAGE COORDINATES:

IMAGE COORDINATES:

WHAT DO YOU NOTICE ABOUT THE COORDINATES?

PRE-IMAGE COORDINATES:

Course 2

8-10 Reflections

IMAGE COORDINATES:

Graphing Reflections on a Coordinate Plane

Graph the reflection of the figure across the y-axis. Write the coordinates of the vertices of the image.

WHAT DO YOU NOTICE ABOUT THE COORDINATES?

To reflect:

Course 2

8-10 Reflections

You must have:- the reflection line (x-axis, y-

axis, or origin)

1. To reflect over the x-axis, multiply your y-value by -1. Leave your x-value alone.

Course 2

8-10 Reflections

2. To reflect over the y-axis, multiply your x-value by -1. Leave your y-value alone.

3. To reflect over the origin, multiply both your x-value AND your y-value by -1.

Example:

Course 2

8-10 Reflections

Pre-Image: A (-4,3) in quadrant II

Reflect over the y-axis

Image: In quadrant I, so x and y are both positive. A’ (4,3)

Course 2

8-10 Reflections

QUESTIONHow are the

coordinates determined from a reflection?

Reflect over the x-axis

Insert Lesson Title Here

3x

y

A

B

C

3

–3

Course 2

8-10 Reflections

Graph the reflection of the triangle ABC across the x-axis. Write the coordinates of the vertices of the image.

The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0).

The coordinates of the vertices of triangle ABC are A’(1, 0), B’(3, –3), C’(5, 0).A’

B’

C’

A’ is read “A prime” and is used to represent the point on the image that corresponds to

point A of the original figure

Reflect over the y-axis

Insert Lesson Title Here

A x

y

B

C

3

3

–3

Course 2

8-10 Reflections

Graph the reflection of the triangle ABC across the y-axis. Write the coordinates of the vertices of the image.

The pre-image coordinates of triangle ABC are A(0,0), B(2,3), C(2,-3).

The coordinates of the vertices of triangle ABC are A’(0, 0), B’(–2, 3), C’(–2, –3).C’

B’

Insert Lesson Title Here

3 x

y

A

B

C

3

–3

Course 2

8-10 Reflections

Graph the reflection of the triangle ABC across the origin. Write the coordinates of the vertices of the image.

The pre-image coordinates of the vertices of triangle ABC are A(1, 1), B(3, 4), C(5, 1).

C’

B’

A’

Reflect over the origin

The coordinates of the vertices of triangle ABC are A’(-1,-1), B’(–3,-4), C’(–5,–1).

K I M

congruent

transformation

reflection