Coordinate Geometry- Plotting points, the cartesian plane and quadrants.

 
2
,
4

 
5
,
1
-5
-5
5
5
 
2
,
2 

 
1
,
7 
The Coordinate Plane
The Coordinate Plane

Learning Objectives:
 Determine the coordinates of a given
point.
 Plot points in the coordinate plane.
 Determine the quadrant for a given
coordinate.

In mathematics, a plane
is a flat surface that goes
on forever in every
direction.
IN ALGEBRA, WE OFTEN USE THE COORDINATE
PLANE OR THE CARTESIAN PLANE

The coordinate plane is
divided by two number lines.
One is horizontal, like the
number line you already know
is called the x-axis.
Left
Right

The other is vertical,
with up being the positive
direction and down being
the negative direction
with zero separating
them.
This is referred to as the
y- axis
Up
Down

The point
where the
two
numberline
means is
called the
origin, (0,0)
NB: The plural of
axis is axes.

The coordinate plane is
filled with points . . .
. . . infinitely many points.

To study a point, we need to
know where to find it. So we give
it coordinates.
Coordinates are like an
address. They tell you how
you can get to a point if you
start at the origin.

y
 
y
x,
x
-5 5
0 10
-10
5
-5
Coordinates are
always written in
parentheses, with
the x-value first
followed by the y-
value.
Coordinates
written in
parentheses are
called an
ordered pair.

-5 5
0 10
-10
5
-5
Consider the
point which has
coordinates,
(4, -2).
Locate the x-value first.
Then the y-value.
The number tells you
how far to move along
the axises.
So, in (4, -2), we need
to move 4 units to the
right followed by 2
units down.
Remember to start
at the origin!
 
y
x,
 
2
,
4 

The two number lines divide the plane
into four regions.
We call the regions quadrants.
Quadrants are labeled with Roman
Numerals.

In Quadrant I, all values
are positive. (+, +)
In Quadrant II, x-values are
negative, while y-values
are positive. (-, +)
In Quadrant III, both x and y
values are negative. (-, -)
In Quadrant IV, x-values
are positive and y-values
are negative. (+, -)
I
II
III IV
-5 5
0 10
-10
5
-5

Plot each point and describe how
to get to the point from the origin.
1. (8,–7)
2. (4,0)
3. (–4,–5)
4. (0,–9)
5. (7,12)
From the origin, move to the
right 8 units, then down 7 units.
From the origin, move to the right 4
units, then stop (Stay on the x-axis.).
From the origin, move to the left 4
units, then down 5 units.
From the origin, don’t move to the right or left (stay
on the y-axis), then move down 9 units.
From the origin, move to the right
7 units, then up 12 units.

 Write the coordinates for each point shown.
A
B
D
F
E
C
A:
B:
C:
D:
E:
F:
(3, 5)
(-3, 3)
(0, 0)
(0, -2)
(2, -3)
(-1, -4)

Plot and label each point. Name the quadrant.
Points
Quadrant
A: (1,4)
B: (-3,5)
C: (3,-5)
D: (-3,-5)
E: (0,-4)
F: (-4,0)
A
B
C
D
E
F
I
II
IV
III
y-axis
x-axis

TRANSFORMATIONS
in the
Coordinate Plane

Learning Objectives:
 Explain the difference between a
transformation and a rigid transformation
 State and describe briefly, the four types
of transformations
 Perform translations of points and objects
on the Cartesian Plane
 Calculate the prime points of a reflection
 Determine the translation vector form the
images provided

A TRANSFORMATION is when a figure or
point is moved to a new position in a coordinate plane.
This move may include a change in size as well as
position.
A RIGID TRANSFORMATION takes
place when the size and shape remain the same but the
figure moves into a new position.

There are four types of movement
(TRANSFORMATIONS):
 TRANSLATION……(Slide)
 REFLECTION……..(Flip)
 ROTATION…….…..(Turn)
 DILATION…(Enlarges or Reduces)

TODAY WE WILL WORK WITH
TRANSLATIONS
STOP AND DO
TRANSLATION ACTIVITY
HTTPS://
WWW.TRANSUM.ORG/SOFTWARE/SW/STARTER_OF_THE_DAY/STUDE
NTS/TRANSFORMATIONS/DRAW.ASP?LEVEL=2
ONCE ACTIVITY IS COMPLETE, WE WILL COME BACK TO THE
POWERPOINT AND ADD TO OUR NOTES.

TRANSLATION is a movement of a figure
that involves a slide in the x and/ y direction on a
coordinate plane. More than one move may take
place. Here is what a translation may look like.
Notice that the direction the triangle is
pointing did not change.

You have discovered
that there are two
methods to perform a
“TRANSLATION”.
Each will give you the
new “prime points”.

METHOD 1:
Example: Plot points
A(-2, 3), B(-6, 3), and
C(-2, 7). Translate the
figure 8 units right and
5 units down.
STEP 1: Plot original
points
STEP 2: From each
original point move 8 units
right and 5 units down.
STEP 3: Connect the
new points. This is your
image and the points are the
“prime” points.
A(-2,3)
A’(6, -2)
B(-6,3)
B’(2, -2)
C(-2,7)
C’(6, 2)
A
B
C
STEP 4:
Now list the location of
the new points as your
“primes”.

METHOD 2:
A right/left move will affect the x coordinate and
an up/down move will affect the y coordinate.
Example: Plot points A(-2, 3), B(-6, 3), and C(-2, 7). If
the figure is translated using a vector of 8
Name the prime points. 5
The 8 units right will add 8 to the x number in
the coordinate set and the 5 units down will
subtract 5 from the y
x y
A(-2,3) -2 + 8 = 6 and 3 – 5 = -2
A’(6, -2)
B(-6,3) -6 + 8 = 2 and 3 – 5 = -2
B’(2, -2)
C(-2,7) -2 + 8 = 6 and 7 – 5 = 2

Quick Questions
 Describe the difference between the pre-image and
image.
 Are the pre-image and image congruent? Similar?
How do you know?
 If you were only given the coordinates of a figure,
how could you determine if it was the pre-image or
image?
 Which coordinate is changed when you translate a
figure to the right or left? Up or down?

Coordinate Geometry- Plotting points, the cartesian plane and quadrants.

More Related Content

Similar to Coordinate Geometry- Plotting points, the cartesian plane and quadrants. (20)

Recently uploaded (20)

Coordinate Geometry- Plotting points, the cartesian plane and quadrants.