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Chapter OneCoordinates and Design
What numbers would you write on this line? Each space is 1 unit
Number LineStudent Outcome: Identify and plot points in the 4 quadrants of
the Cartesian plan using ordered pairs
0
What numbers would you write on this line?
Each space is 1 unit
Number LineStudent Outcome: Identify and plot points in the 4 quadrants
of the Cartesian plan using ordered pairs
0
The Cartesian Plane (or coordinate grid) is made up of two number lines that intersect perpendicularly at their respective zero points.
Cartesian PlaneStudent Outcome: Identify and plot points in the 4 quadrants of the
Cartesian plan using ordered pairs
ORIGINThe point where the x-axis and the y-axis cross(0,0)
The horizontal axis is called the x-axis.
The vertical axis is called the y-axis.
Parts of a Cartesian PlaneStudent Outcome: Identify and plot points in the 4 quadrants of the
Cartesian plan using ordered pairs
The Coordinate Grid is made up of 4 Quadrants.
QuadrantsStudent Outcome: Identify and plot points in the 4 quadrants
of the Cartesian plan using ordered pairs
QUADRANT IQUADRANT II
QUADRANT III QUADRANT IV
The signs of the quadrants are either positive (+) or negative (-).
Signs of the QuadrantsStudent Outcome: Identify and plot points in the 4 quadrants of the
Cartesian plan using ordered pairs
QUADRANT IQUADRANT II
QUADRANT III QUADRANT IV
(+, +)(-, +)
(-, -) (+, -)
1.1 The Cartesian PlaneStudent Outcome: Identify and plot points in the 4 quadrants of the
Cartesian plan using ordered pairs
Identify Points on a Coordinate Grid
A: (x, y)
B: (x, y)
C: (x, y)
D: (x, y)
.
1.1 The Cartesian PlaneStudent Outcome: Identify and plot points in the 4 quadrants of the
Cartesian plan using ordered pairs
Identify Points on a Coordinate Grid
A: (5, 7)
B: (5, 3)
C: (9, 3)
D: (9, 7)
When we read coordinates we read them in the order x then y
Plot the following pointson the smart boardA: (9, -2)B: (7, -5)C: (2, -4)D: (2, -1)E: (0, 1)F: (-2, 3)G: (-7, 4)
What are common mistakes when constructing a Coordinate Plane?
1. Units not the same in terms of intervals2. Switch the order that they appear3. Wrong symbols for quadrants
Textbook: Page 9
#5, 7, for questions 9 and 10 plot on two separate graphs. Graph paper is provided for you.
Challenge #14, 16
Assignment
Practical Quiz #1
1.2 Create DesignsStudent Outcome: I will understand the relationship between
vertex and ordered pairs
Put your thinking cap on!What is the following question asking us to find?
Label each vertex of each shape.
Question!What is a vertex?
1.2 Create DesignsStudent Outcome: I will understand the relationship between
vertex and ordered pairs
What is a vertex?
AB
C
•A vertex is a point where two sides of a figure•meet.•The plural is vertices!
The vertices of the Triangle areA (x, y)B (x, y)C (x, y)
A (4, 4)
B (0, 4)
C (2, 0)
Graphic Artists use coordinate grids to help them make certain designs. Flags, corporate logos can all be constructed through the use of our coordinate grids.
Create DesignsStudent Outcome: I will understand the relationship between
vertex and ordered pairs
1.2 Create Designs
Study the following Flag. How many vertices can you find in the
design. Imagine seeing this on a coordinate grid. Notice how it is centered and equally
distributed on each side.
1.2 Create Designs Assignment: You have been hired to create a flag for the company
“Flags R Us!” They are looking for a new creative design that can be based on an interest or hobby of yours. The flag design can be a cool pattern or related to any sport, hobby, or activity you are involved with.
The flag needs to have a minimum of 10 Vertices. They want a detailed location of any 10 vertices located
on the bottom of your design (list the coordinates). It is your responsibility to use a coordinate grid to
create your own pattern.
Evaluation
Your Flag will be evaluated as following”◦ Neatness: (Have you made sure to color inside the lines).
◦ Vertices: (Do you have at least 10).
◦ Design: (Have you used designs and shapes to create an image).
◦ Handout: (Do you have all the vertices clearly labeled in a legend).
Student Name:
10 VerticesA) D) G) J)B) E) H)C) F) I)
BLM 1-3, BLM 1-4, BLM 1-5, BLM 1-6
Review Through Assignment
1.3 TRANSFORMATIONS
This section will focus on the use of Translations, Reflections, Rotations, and
describe the image resulting from a transformation.
1.3 TransformationsStudent Outcome: I can perform and describe transformations of a 2-D
shape in all 4 quadrants of a Cartesian plane.
Transformations:◦ Include translations, reflections, and rotations.
Translation Reflection Rotation
Translations are SLIDES!!!
Translation
Let's examine some translations related to coordinate geometry.
1.3 TransformationsStudent Outcome: I can perform and describe transformations of a 2-D
shape in all 4 quadrants of a Cartesian plane.
Translation:◦ A slide along a straight
line
Count the number of horizontal units and vertical units represented by the translation arrow.
The horizontal distance is 8 units to the right, and the vertical distance is 2 units down (+8 -2)
1.3 TransformationsStudent Outcome: I can perform and describe transformations of a 2-D shape in all 4 quadrants of a Cartesian
plane. Translation:
◦ Count the number of horizontal units the image has shifted.
◦ Count the number of vertical units the image has shifted.
We would say the Transformation is:
1 unit left,6 units up or
(-1+,6)
In this example we have moved each vertex 6 units along a straight line. If you have noticed the corresponding A is now labeled A’
What about the other letters?
A translation "slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction
When you are sliding down a water slide, you are experiencing a translation. Your body is moving a given distance (the length of the slide) in a given direction. You do not change your size, shape or the direction in which you are facing.
1.3 Transformations: Let’s Practice
Textbook Page 25
◦ Question #4a, b, 5,
1.3 TranslationsStudent Outcome: I can perform and describe transformations of a 2-D
shape in all 4 quadrants of a Cartesian plane.
4 a) What is the translation shown in this picture?
6 units right, 5 units up Or
(+6,+5)
1.3 TranslationsStudent Outcome: I can perform and describe transformations of a 2-D
shape in all 4 quadrants of a Cartesian plane.
4 b) What is the translation in the diagram below?
Horizontal Distance is:6 units left
Vertical Distance is:4 units up
Or(-6,+4)
1.3 TranslationsStudent Outcome: I can perform and describe transformations of a 2-D
shape in all 4 quadrants of a Cartesian plane.
#5 B) The coordinates of the translation image are
◦ P'(+7, +4), Q’(+7, –2), ◦ R'(+6, +1), S'(+5, +2).
C) The translation arrow is shown: 3 units right and 6 units down. (+3, -6)
Reflections Is figure A’B’C’D’ a reflection image of figure
ABCD in the line of reflection, n? How do you know?
Figure A'B'C'D' IS a reflection image of figure ABCD in the line of reflection, n.
Each vertex in the red figure is the same distance from the line of reflection, n, as its reflected vertex in the blue image.
A reflection is often called a flip. Under a reflection, the figure does not change size. It is simply flipped over the line of reflection.
Reflecting over the x-axis:
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite.
Reflecting over the y-axis:Where do you think this picture will end up?
Practical Quiz #2
Practical Quiz #2
Reflections Assignment
Page 25 Lets go over #7 and #8 as a class.
Page 26 #10,11, and12 on your own!
Reflection Question #10
Reflection Question #11The coordinates of A'B'C'D'E'F'G'H' are:
◦ A’(+2,+2) B’(0,+2)
C’(0,-5)
D’(+2, –5),
E'(+2, –4), F'(+3, –4),
G'(+3, –2), H'(+2, –2).
Reflection Question #12
TransformationsRotation:A turn about a fixed point called “the center of rotation”The rotation can be clockwise or counterclockwise
1.3 TransformationsStudent Outcome: I can perform and describe transformations of a 2-D
shape in all 4 quadrants of a Cartesian plane.
Rotation:◦A turn about a fixed point called “the
center of rotation”◦The rotation can be clockwise or
counterclockwise.
Transformations Assignment
Page 27 Lets go over #13 and #14 as a class.
Page 27-28 # 15,16,17, and18 on your own!
1.3 Transformations Pg 27. #13
a) The coordinates for ∆HAT are H(–3, –2), A(–1, –3), and T(–3, –6).
The coordinates for ∆HAT are H(–3, –2), A(–1, –3), and T(–3, –6).
b) The rotation is 180 counterclockwise.
Rotations
Pg 27 #15.a) The coordinates for the centre of rotation are (–4, –4).
b) Rotating the figure 90° clockwise will produce the same image as rotating it 270° in the opposite direction, or counterclockwise.
Homework Questions #16
a) The coordinates for the centre of rotation are (+2, –1).
b) The direction and angle of the rotation could be 180° clockwise or 180° counterclockwise.
Homework Questions #17
a) The figure represents the parallelogram rotated about C, 270° clockwise.
b) The coordinates for Q'R'S'T' are Q'(–1, –1), R'(–1, +2), S'(+1, +1), and T'(+1, –2).
Homework Questions # 18
b) The rotation image is identical to the original image.
by D. Fisher
Geometric Transformations
REFLECTION
Why is this not perfect reflection?
Why is this not perfect reflection?Zebras have slightly different stripping, Ears not similar, leg bent different.
Reflection, Rotation, or Translation
1.
Reflection, Rotation, or Translation
1.
Reflection, Rotation, or Translation
2.
Reflection, Rotation, or Translation
2.
Reflection, Rotation, or Translation
3.
Reflection, Rotation, or Translation
3.
REFLECTION
Reflection, Rotation, or Translation
4.
Reflection, Rotation, or Translation
4.
REFLECTION
Reflection, Rotation, or Translation
5.
Reflection, Rotation, or Translation
5.
ROTATION
Reflection, Rotation, or Translation
6.
Reflection, Rotation, or Translation
6
TRANSLATION – MOVE FROM ONE POINT TO
ANOTHER
Reflection, Rotation, or Translation
7.
Reflection, Rotation, or Translation
7.
Reflection, Rotation, or Translation
11.
PROBABLY DOESN’T FIT ANY CATEGORY
Reflection, Rotation, or Translation
12.
TRANSLATION
Reflection, Rotation, or Translation
13.
Why possibly both? Either reflected or
rotated 180°
Reflection, Rotation, or Translation
14.
ROTATION
Reflection, Rotation, or Translation
15.
REFLECTION IN SEVERAL DIRECTIONS
Reflection, Rotation, or Translation
16.
ROTATION
Reflection, Rotation, or Translation
17.
Reflection, Rotation, or Translation
18.
Reflection, Rotation, or Translation
19.
Reflection in multiple mirrors.
Reflection, Rotation, or Translation
20.
Reflection, Rotation, or Translation
21.
Reflection, Rotation, or Translation
22.
Transformations Assignment
Page 36-37 # 1-10, 12, 15, 16, 18 and 21 on your own!
The Ultimate PowerPoint Game
Each team will hide their 4 battleships in their HIDDEN Mathematical Ocean by writing the correct number of points for each battleship with its corresponding letter
All ships must be either horizontal or vertical
Ships may not overlap
Draw a rectangle around the correct number of points for each battleship
BattleGraph Directions
BattleGraph Example
This is the INSIDE board.
Keep this board HIDDEN
from the other team!
ATTACKERS & DEFENDERS Teams will take turns being the ATTACKERS and the
DEFENDERS
The ATTACKERS will select a place to attack by giving an ordered pair of numbers to the DEFENDERS
The ATTACKERS will then write the ordered pair in the box to the side and circle that point on their VISIBLE Mathematical Ocean
The DEFENDERS will find the coordinate on their HIDDEN Mathematical Ocean and circle it
The DEFENDERS will say if the attack was a HIT (ATTACKERS fill-in circle) or a MISS (ATTACKERS leave circle empty)
Teams will then switch roles
Winning BattleGraph If the coordinate is not written in the box on the
side, the attack is automatically a MISS
If the coordinate is not in the Mathematical Ocean, the attack is automatically a MISS
If the ATTACKERS sink one of your battleships, you must tell tell them. Otherwise you will LOSE one turn.
The ATTACKERS will connect the points once the entire ship is SUNK.
To WIN the game you must sink all of the the other team’s battleships before they sink all of yours
BattleGraph Example
Use this board to ATTACK.
Keep this board VISIBLE!
This is the OUTSIDE board.
Get Ready to Hide Your Battleships
Aircraft Carrier(5 A points)
Cruiser(4 C points)
Destroyer(3 D points)
Submarine(2 S points)
on the HIDDEN Mathematical Ocean
Use this board to
HIDE your battleship
s.
Keep this board
HIDDENfrom the
other team!
This is the INSIDE board.
Battleships1 Aircraft Carrier (AAAAA)1 Cruiser
(CCCC)1 Destroyer
(DDD)1 Submarine
(SS)
Home Page
Use this board to ATTACK.
Keep this board VISIBLE!
This is the OUTSIDE board.