Welcome Back!
 Pick up papers from the front table
 Start reading the writing prompt.
 Tell your tablemates about one thing you did over the break.
.
3 THINGS
NEW JOBS
Paper Passer
Time Keeper
MATH HISTORY
Fibbonacci
GO OVER UNIT 1 TEST
Look at the score over /25
A= 22.5- 25
B= 20- 22
C= 17.5- 19.5
Below a 17.5 please come see me!
AVERAGES
Period 1
•20.7/ 25= 83%
Period 3
•19/ 25= 76%
Period 4
•20.2/25= 81%
FALL WRITING
ASSIGNMENT
Pre-Test on Coordinate Planes
 Take out a piece of paper and split it among your group
members (each person needs a quarter sheet of paper)
 Before break, I said that it is extremely important to know
the coordinate plane.
 This is to see how well you know it. This will not effect your
grade. Try your best.
Pre-Test on Coordinate Planes
1. Draw a coordinate plane
2. Label the x-axis, y- axis, and origin. Label -5 to 5 on
both axes. Also, label the quadrants.
3. On that same coordinate plane that you drew in #1 label
the following points.
A. (0, 0)
B. (-3, 0)
C. (-4, -1)
D. (2, 5)
CHECK YOUR
ANSWERS!
1. Now you are going to critique your partners.
2. What did they do correct? What do you think they should fix?
3. Now, grade your own coordinate plane from the example on
the document camera.
4. Pass it in.
1.7: TRANSFORMATIONS
IN THE COORDINATE
PLANE
SWBAT identify reflections, rotations and
translation.
MATH JOKE OF THE
DAY
Spanish Teacher: Why didn’t you translate the verb?
Student: I did, I moved it 3 units to the right and 2 units up.
1-7 Transformations in the Coordinate Plane
Take 1 minute to brainstorm in your notes on what you
remember about the word Transformations.
Share your brainstorming with your tablemates. I will be calling
on random students using the equity sticks to share pieces of
your brainstorm.
1-7 Transformations in the Coordinate Plane
Transformation:
• a change in the position, size, or shape of a figure.
Pre-Image:
• The original figure .
Image:
• New figure.
Types of Transformations
Types of Transformations
(1) Reflection
- a flip
(2) Translation - a slide
- a turn
(3) Rotation
(4) Dilation – We will not be learning this quite yet.
APK: 1.7: Transformations in the
Coordinate Plane
 Take out your whiteboards.
 Each tablemate will draw a different transformation.
o For example: Dante will draw a reflection, Yasmine will
draw a rotation, Vicky will draw a dilation, and Juan will
draw a translation.
o If you are a table of three, then you can leave out one
transformation.
 On each whiteboard, you will need to label the pre-image
and image.
 You will only have 2 minutes to complete.
CFU:Whiteboards
What is the name of the original figure, before it is
transformed?
Pre – Image
What is the name of the transformed figure?
Image
1-7 Transformations in the Coordinate Plane
What is the big difference between a dilation and a
reflection/translation/rotation?
Types of Transformations
(1) Reflection
(2) Translation
(3) Rotation
Isometry – A transformation that does
not change the size or shape of a
figure.
(4) Dilation- changes size
Important:
A transformation maps the pre-image to the image.
Arrow Notation – used to describe a transformation.
Pre-image  Image
We use primes (‘) to label the image
1-7 Transformations in the Coordinate Plane
Please copy the following pre-image and image. Arrow notation
is used at the bottom of the figure to tell the reader how the
pre-image was transformed.
1-7 Transformations in the Coordinate Plane
Example 1
Draw this in your notes. Identify each transformation. Use
arrow notation to describe the transformation.
(a)
translation; MNOP  M N O P
(b)
rotation; ∆XYZ  ∆X Y Z
Whiteboards
Identify the transformation. Then use arrow notation to
describe the transformation.
90° rotation, ∆ABC  ∆A B C
In your Notes:
Example 2
A figure has vertices at A(1, -1), B(2, 3), and C(4, -2). After a
transformation, the image of the figure has vertices at A’(-1, -1),
B’(-2, 3), and C’(-4, -2).
 Draw the pre-image and image.
 Identify the transformation.
 Use arrow notation to describe the transformation.
CHECK YOUR WORK!
Reflection:
ABC A’B’C’
Whiteboards
A figure has vertices at E(2, 0), F(2, -1), G(5, -1), and H(5, 0).
After a transformation, the image of the figure has vertices at
E’(0, 2), F’(1, 2), G’(1, 5), and H’(0, 5).
1. Draw the pre-image and image.
2. Identify the transformation.
3. Use arrow notation to describe the transformation.
The transformation is a 90°
counterclockwise rotation.
EFGH E’F’’G’H’
Translations:
• add a to the x-coordinates of the
preimage
• add b to the y-coordinates of the
preimage.
• Rule: (x, y)  (x + a, y + b).
Example 3:
Find the coordinates for the image of ∆ABC after the
translation (x, y)  (x + 2, y - 1). Draw the image.
Step 1 Find the coordinates of
∆ABC.
The vertices of ∆ABC are A(–4, 2), B(–3, 4),
C(–1, 1).
Example 3: Translations in the Coordinate Plane
Find the coordinates for the image of ∆ABC after the
translation (x, y)  (x + 2, y - 1). Draw the image.
Step 1 Find the coordinates of
∆ABC.
The vertices of ∆ABC are A(–4, 2), B(–3, 4),
C(–1, 1).
Example 3 Continued
Step 2 Apply the rule to find the vertices of the image.
A (–4 + 2, 2 – 1) = A (–2, 1)
B (–3 + 2, 4 – 1) = B (–1, 3)
C (–1 + 2, 1 – 1) = C (1, 0)
Step 3 Plot the points. Then finish
drawing the image by using a
straightedge to connect the vertices.
Whiteboards
Find the coordinates for the image of JKLM after the translation
(x, y)  (x – 2, y + 4)..
The vertices of JKLM are J(1, 1), K(3, 1), L(3, –
4), M(1, –4), .
.
J (–1, 5)
K (1, 5)
L (1, 0)
M (–1, 0)
Example 4: Art History Application
The figure shows part of a tile floor. Write a rule for the
translation of hexagon 1 to hexagon 2.
Step 1 Choose two points.
Choose a Point A on the preimage and a
corresponding Point A on the image. A
has coordinate (2, –1) and A has
coordinates
A
A
Talk with your table mates to come up with a rule!
Rule:
(x, y) → (x – 3, y + 1.5 )
1-7 Transformations in the Coordinate Plane
Example 4
The picture below shows half of a stenciled design. The full
design should resemble a sun. Name two transformations that
can be performed on the image so that the image and its preimage form a complete picture. Be as specific as possible,
referring to L and P.
Talk with your table!
1-7 Transformations in the Coordinate Plane
Example 5
(a) What transformation is suggested by the wings of an
airplane?
(b) What transformation is suggested by a person climbing a
ladder?
(c) What transformation is suggested by a Ferris wheel?
Check For Understanding
o Take out a half sheet of graph paper.
o Put your name, the date, and period in the upper right.
o Title your graph paper “1.7 CFU.”
o Answer the questions on your own.
1. A figure has vertices at X(-1, 1), Y(1, 4), and Z(2, 2). After a
transformation, the image of the figure has vertices at X’(-3, 2), Y’(-1, 5),
and Z’(0, 3).
 Draw the pre-image and image.
 Identify the transformation.
 Use arrow notation to describe the transformation.
2. What transformation is suggested by an image in water.
WHEN ARE WE EVER
GOING TO HAVE TO USE
THIS?
Computer animations
http://www.youtube.com/watch?v=dVtz55mIuz4
0-1:37