Transcript Chapter One - Notre Dame Academy

Coordinates and Design

The Cartesian Plane (or coordinate grid) is
made up of two directed real lines that
intersect perpendicularly at their respective
zero points.
ORIGIN
The point where
the x-axis and
the y-axis cross
(0,0)

The horizontal axis is called the x-axis.
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The vertical axis is called the y-axis.

The Coordinate Grid is made up of 4
Quadrants.
QUADRANT II
QUADRANT I
QUADRANT III
QUADRANT IV
The signs of the quadrants are either
positive (+) or negative (-).
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QUADRANT II
(-, +)
QUADRANT III
(-, -)
QUADRANT I
(+, +)
QUADRANT IV
(+, -)
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Identify Points on a Coordinate Grid
A: (x, y)
B: (x, y)
C: (x, y)
D: (x, y)

.
1.1 The Cartesian Plane
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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 points
on the smart board
A: (9, -2)
B: (7, -5)
C: (2, -4)
D: (2, -1)
E: (0, 1)
F: (-2, 3)
G: (-7, 4)
1.
2.
3.
Units not the same in terms of intervals
Switch the order that they appear
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
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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?
What is a vertex?
•A vertex is a point where two sides of a figure
•meet.
•The plural is vertices!
B
A
C
The vertices of the Triangle are
A (4, 4)
A (x, y)
B (0, 4)
B (x, y)
C (2, 0)
C (x, y)

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.
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
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.

On page 12 of your text an assignment is
given to draw a flag. Plot the points with the
proper labels and color the inside of the flag
design red. Graph paper is supplied to you.
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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.

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 Vertices

BLM 1-3, BLM 1-4, BLM 1-5, BLM 1-6
This section will focus on the use of
Translations, Reflections, Rotations, and
describe the image resulting from a
transformation.

Transformations:
◦ Include translations, reflections, and rotations.
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Translation
Reflection
Rotation

Translations are SLIDES!!!
Let's examine some translations related to coordinate geometry.
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Translation:
◦ A slide along a straight line
Count the number of horizontal units
and vertical units represented by the
translation arrow.
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The horizontal distance is 8 units to the right, and the vertical distance is 2 units down
(+8 -2)

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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.
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Let’s Practice
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Textbook Page 25
◦ Question #4a, b, 5,

4 a) What is the translation shown
in this picture?
6 units right, 5 units up
Or
(+6,+5)
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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)
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#5
B) The coordinates of the
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translation image are
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◦ P'(+7, +4), Q’(+7, –2),
◦ R'(+6, +1), S'(+5, +2).
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C) The translation arrow is
shown: 3 units right and
6 units down. (+3, -6)
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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 xaxis, the xcoordinate remains
the same, but the ycoordinate is
transformed into its
opposite.
Reflecting over the y-axis:
Where do you think this
picture will end up?
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Assignment
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Page 25
Lets go over #7 and #8 as a class.
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Page 26 #10,11, and12 on your own!
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Question #10
Question #11
The coordinates of A'B'C'D'E'F'G'H' are:
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◦ A’(+2,+2)  E'(+2, –4),
 B’(0,+2)  F'(+3, –4),
 C’(-4,-5)
 D’(+2, –5),
G'(+3, –2),
 H'(+2, –2).
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Question #12
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Rotation:
◦ A turn about a fixed point called “the center of
rotation”
◦ The rotation can be clockwise or counterclockwise.
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Assignment
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Page 27
Lets go over #13 and #14 as a class.
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Page 27-28 # 15,16,17, and18 on your own!
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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.
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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.
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#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.
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#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).
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# 18
b) The rotation image is identical to
the original image.
by D. Fisher
1.
1.
2.
2.
3.
Reflection, Rotation, or
Translation
3.
Reflection, Rotation, or
Translation
4.
4.
5.
Reflection, Rotation, or
Translation
5.
Reflection, Rotation, or
Translation
7.
7.
6.
Reflection, Rotation, or
Translation
8.
Reflection, Rotation, or
Translation
10.
10.
ZEBRAS HAVE
SLIGHTLY
DIFFERENT
STRIPING
11. Reflection, Rotation, or
Translation
PROBABLY
DOESN’T FIT
ANY
CATEGORY
12. Reflection, Rotation, or
Translation
13. Reflection, Rotation, or
Translation
Why possibly both?
Either reflected or
rotated 180°
14. Reflection, Rotation, or
Translation
15. Reflection, Rotation, or
Translation
REFLECTION
IN SEVERAL
DIRECTIONS
16. Reflection, Rotation, or
Translation
17. Reflection, Rotation, or
Translation
18. Reflection, Rotation, or
Translation
19.
Reflection, Rotation, or
Translation
Reflection in multiple mirrors.
20. Reflection, Rotation, or
Translation
21. Reflection, Rotation, or
Translation
22. Reflection, Rotation, or
Translation

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
Keep this board
This is the INSIDE
board.
HIDDEN
from the other
team!
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
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
Keep this board
VISIBLE!
Use this board to
ATTACK.
This is the
OUTSIDE board.
Aircraft Carrier
(5 A points)
Cruiser
(4 C points)
Destroyer
(3 D points)
Submarine
(2 S points)
on the HIDDEN
Mathematical Ocean
Battleships
1 Aircraft Carrier
(AAAAA)
1 Cruiser
(CCCC)
1 Destroyer
(DDD)
1 Submarine
(SS)
Use this
board to
HIDE your
battleships.
Keep this
board
HIDDEN
from the
other team!
This is the
INSIDE
board.
Home Page
Use this board to
ATTACK.
Keep this board
VISIBLE!
This is the OUTSIDE
board.