Transcript The Coordinate Plane

The Coordinate Plane
1.10 p. 50
Learn to locate and graph points on the
coordinate plane, name the coordinates of
points, and identify the quadrants.
The objectives in this lesson will be used
as we graph linear functions and solve
systems of equations. Please learn the
terms that are used as we practice the
skills.
Vocabulary
coordinate plane
axes
x-axis
y-axis
quadrants
origin
ordered pair
x-coordinate
y-coordinate
These definitions will be covered
throughout the lesson. We will
review them at the end of class.
A coordinate plane is formed by two number
lines in a plane that intersect at right angles. The
point of intersection is the zero on each number
line.
• The two number lines are called the axes.
• Use this diagram to complete the
labels on the coordinate plane in
your notes.
• Each section of the diagram will be
discussed during the next few slides.
• The horizontal axis is
called the x-axis.
• The vertical axis is
called the y-axis.
• The two axes divide
the coordinate plane
into four quadrants.
• Please notice that
Roman numerals are
used to label the
quadrants.
• The point where the
axes intersect is
called the origin.
• Its coordinates are
(0,0)
An ordered pair gives the location of a point
on a coordinate plane. The first number tells
how far to move right (positive) or left
(negative) from the origin. The second
number tells how far to move up (positive) or
down (negative).
The numbers in an ordered pair are called
coordinates. The first number is called the
x-coordinate. The second number is called
the y-coordinate.
The ordered pair for the origin is (0,0).
Identifying Quadrants
Name the quadrant where each point is
located.
What about point Z?
A. X
Quadrant IV
B. Y
Quadrant III
C. S
Quadrant II
D. V
Quadrant I
Helpful Hint
Points on the axes are not in any quadrant.
Locating Points on a Coordinate Plane
Give the coordinates of each point.
A. X
From the origin, X is 4 units
right and 1 unit down.
(4, –1)
B. Y
From the origin, Y is 2 units
left, and 3 units down.
(–2, –3)
Locating Points on a Coordinate Plane
Give the coordinates of each point.
C. S
From the origin, S is 3 units
left, and 3 units up.
(–3, 3)
D. V
From the origin, V is 4 units
right and 2 units up. (4, 2)
Points that are located on an axis may cause confusion. Look along
the x-axis……..where do you have to stop to align with the point???
E. Z
From the origin, Z is 0 units
right, and 4 units up.
(0, 4)
C. T
From the origin, T is 1 unit
right, and 3 units down.
(1, –3)
A positive y-value moves us up.
A negative x-value moves us to the
left.
A positive
x-value moves us to the right.
x
A negative y-value moves us down.
( x, y )
y
( x,y )
( x,y )
(+ ,+ )
(
,
)
I
( -,+ )
(
,
)
II
( - , - )
(
,
)
III
(+ , - )
(
,
)
IV
Quadrant??
Let’s go back to the first page of your notes
and put these signs in the appropriate
quadrant.
Learn to associate the (x,y) signs with the quadrant.
(-,+)
y
(+,+)
x
(-,-)
Now let’s graph…...
(+,-)
Graphing Points on a Coordinate Plane
Graph each point on a coordinate plane.
M(4, 3)
From the origin, move 4
units right, and 3 units up.
Q (–4, 1)
From the origin, move 4
units left, and 1 unit up.
R (0, -3)
From the origin, move 3
units down.
y
4
Q
M
2
x
–4
–2
0
–2
–4
2
.R
4
Graph each point on a coordinate plane.
L(3, 4) From the origin, move 3
units right, and 4 units up.
y
N (–3, –3)
From the origin, move 3
units left, and 3 units down.
P (1, –2)
From the origin, move 1
unit right and 2 units down.
4
L
2
x
–4
–2
N
0
2
–2
P
–4
4
Lesson Quiz
Name the quadrant where each ordered pair
is located.
1. (3, –5) IV
2. (–4, –2) III
3. (6, 2) I
4. (–7, 9)
II
Give the coordinates of each
point.
5. A (–2, 3)
6. B (1, 2)
7. C (0, –2)
8. D (–2, –3)
y
E
D
Graph these points
H
A (4, 0)
G
A
B
F
C
x
E ( -3, 5)
B(-2, -2)
F( 3, -4)
C (0, -5)
G (0, 0)
D(4, 4)
H ( -4, 2)
What have we accomplished?
• We have graphed locations on the
coordinate plane using ordered pairs
(coordinates).
• We have identified the regions on the
plane as quadrants.
• We have used coordinates to identify
points.