The Coordinate Plane

1
The Coordinate Plane
What You'll Learn
You will learn to name and graph ordered pairs on
acoordinate plane.
In coordinate geometry, grid paper is used to
locate points.
The plane of the grid is called the coordinate
plane.
2
The Coordinate Plane
What You'll Learn
You will learn to name and graph ordered pairs on
acoordinate plane.
In coordinate geometry, grid paper is used to
locate points.
The plane of the grid is called the coordinate
plane.
3
The Coordinate Plane
The horizontal number lineis called the ______.
4
The Coordinate Plane
The horizontal number lineis called the ______.
x-axis
5
The Coordinate Plane
The horizontal number lineis called the ______.
x-axis
The vertical number lineis called the ______.
6
The Coordinate Plane
The horizontal number lineis called the ______.
x-axis
The vertical number lineis called the ______.
y-axis
7
The Coordinate Plane
The horizontal number lineis called the ______.
x-axis
The vertical number lineis called the ______.
y-axis
The point of intersection of the twoaxes is
called the _____.
8
The Coordinate Plane
The horizontal number lineis called the ______.
x-axis
The vertical number lineis called the ______.
y-axis
The point of intersection of the twoaxes is
called the _____.
origin
9
The Coordinate Plane
The horizontal number lineis called the ______.
x-axis
The vertical number lineis called the ______.
y-axis
The point of intersection of the twoaxes is
called the _____.
origin
The two axes separate the plane intofour regions
called _________.
10
The Coordinate Plane
The horizontal number lineis called the ______.
x-axis
The vertical number lineis called the ______.
y-axis
The point of intersection of the twoaxes is
called the _____.
origin
The two axes separate the plane intofour regions
called _________.
quadrants
11
The Coordinate Plane
An ordered pair of real numbers, called
coordinates of a point, locates apoint in the
coordinate plane.
12
The Coordinate Plane
An ordered pair of real numbers, called
coordinates of a point, locates apoint in the
coordinate plane.
Each ordered pair corresponds to EXACTLY ________
in the coordinate plane.
13
The Coordinate Plane
An ordered pair of real numbers, called
coordinates of a point, locates apoint in the
coordinate plane.
one point
Each ordered pair corresponds to EXACTLY ________
in the coordinate plane.
14
The Coordinate Plane
An ordered pair of real numbers, called
coordinates of a point, locates apoint in the
coordinate plane.
one point
Each ordered pair corresponds to EXACTLY ________
in the coordinate plane.
The point in the coordinate plane is called the
graph of the ordered pair.
15
The Coordinate Plane
An ordered pair of real numbers, called
coordinates of a point, locates apoint in the
coordinate plane.
one point
Each ordered pair corresponds to EXACTLY ________
in the coordinate plane.
The point in the coordinate plane is called the
graph of the ordered pair.
Locating a point on the coordinate plane is
called _______ the ordered pair.
16
The Coordinate Plane
An ordered pair of real numbers, called
coordinates of a point, locates apoint in the
coordinate plane.
one point
Each ordered pair corresponds to EXACTLY ________
in the coordinate plane.
The point in the coordinate plane is called the
graph of the ordered pair.
graphing
Locating a point on the coordinate plane is
called _______ the ordered pair.
17
The Coordinate Plane
An ordered pair of real numbers, called
coordinates of a point, locates apoint in the
coordinate plane.
one point
Each ordered pair corresponds to EXACTLY ________
in the coordinate plane.
The point in the coordinate plane is called the
graph of the ordered pair.
graphing
Locating a point on the coordinate plane is
called _______ the ordered pair.
Postulate 2 4 Completeness Property for Points in the Plane Each point in a coordinate plane corresponds to exactly one __________________________. Each ordered pair of real numbers corresponds to exactly one __________________________.
18
The Coordinate Plane
An ordered pair of real numbers, called
coordinates of a point, locates apoint in the
coordinate plane.
one point
Each ordered pair corresponds to EXACTLY ________
in the coordinate plane.
The point in the coordinate plane is called the
graph of the ordered pair.
graphing
Locating a point on the coordinate plane is
called _______ the ordered pair.
Postulate 2 4 Completeness Property for Points in the Plane Each point in a coordinate plane corresponds to exactly one __________________________. Each ordered pair of real numbers corresponds to exactly one __________________________.
ordered pair of real numbers
19
The Coordinate Plane
An ordered pair of real numbers, called
coordinates of a point, locates apoint in the
coordinate plane.
one point
Each ordered pair corresponds to EXACTLY ________
in the coordinate plane.
The point in the coordinate plane is called the
graph of the ordered pair.
graphing
Locating a point on the coordinate plane is
called _______ the ordered pair.
Postulate 2 4 Completeness Property for Points in the Plane Each point in a coordinate plane corresponds to exactly one __________________________. Each ordered pair of real numbers corresponds to exactly one __________________________.
ordered pair of real numbers
point in the coordinate plane
20
The Coordinate Plane
Graphing an ordered pair, (point) (x, y)
Graph point A at (4, 3)
The first number, 4, is called the ___________.
x-coordinate
It tells the number of units the point lies
tothe __________ of the origin.
21
The Coordinate Plane
Graphing an ordered pair, (point) (x, y)
Graph point A at (4, 3)
The first number, 4, is called the ___________.
x-coordinate
It tells the number of units the point lies
tothe __________ of the origin.
left or right
22
The Coordinate Plane
Graphing an ordered pair, (point) (x, y)
Graph point A at (4, 3)
The first number, 4, is called the ___________.
x-coordinate
It tells the number of units the point lies
tothe __________ of the origin.
left or right
The second number, 3, is called the ___________.
y-coordinate
It tells the number of units the point lies
_____________ the origin.
23
The Coordinate Plane
Graphing an ordered pair, (point) (x, y)
Graph point A at (4, 3)
The first number, 4, is called the ___________.
x-coordinate
(4, 3)
It tells the number of units the point lies
tothe __________ of the origin.
left or right
The second number, 3, is called the ___________.
y-coordinate
It tells the number of units the point lies
_____________ the origin.
above or below
24
The Coordinate Plane
Graphing an ordered pair, (point) (x, y)
Graph point A at (4, 3)
The first number, 4, is called the ___________.
x-coordinate
(4, 3)
It tells the number of units the point lies
tothe __________ of the origin.
left or right
The second number, 3, is called the ___________.
y-coordinate
It tells the number of units the point lies
_____________ the origin.
above or below
What is the coordinate of the origin?
25
The Coordinate Plane
Graphing an ordered pair, (point) (x, y)
Graph point A at (4, 3)
The first number, 4, is called the ___________.
x-coordinate
(4, 3)
It tells the number of units the point lies
tothe __________ of the origin.
left or right
The second number, 3, is called the ___________.
y-coordinate
It tells the number of units the point lies
_____________ the origin.
above or below
What is the coordinate of the origin?
26
The Coordinate Plane
Graphing an ordered pair, (point) (x, y)
Graph point B at (2, 3)
27
The Coordinate Plane
Graphing an ordered pair, (point) (x, y)
Graph point B at (2, 3)
The first number, 2, is called the ___________.
x-coordinate
It tells the number of units the point lies
tothe __________ of the origin.
28
The Coordinate Plane
Graphing an ordered pair, (point) (x, y)
Graph point B at (2, 3)
The first number, 2, is called the ___________.
x-coordinate
It tells the number of units the point lies
tothe __________ of the origin.
left or right
29
The Coordinate Plane
Graphing an ordered pair, (point) (x, y)
Graph point B at (2, 3)
The first number, 2, is called the ___________.
x-coordinate
It tells the number of units the point lies
tothe __________ of the origin.
left or right
The second number, 3, is called the ___________.
y-coordinate
It tells the number of units the point lies
_____________ the origin.
30
The Coordinate Plane
Graphing an ordered pair, (point) (x, y)
Graph point B at (2, 3)
The first number, 2, is called the ___________.
x-coordinate
It tells the number of units the point lies
tothe __________ of the origin.
left or right
The second number, 3, is called the ___________.
y-coordinate
(2, 3)
It tells the number of units the point lies
_____________ the origin.
above or below
31
The Coordinate Plane
Give the coordinates of the points A, B, C,
D
A
B
Point A(x, y)
Point B(x, y)
Point C(x, y)
Point D(x, y)
C
D
32
The Coordinate Plane
Name the points A, B, C, D
A
(3, 2)
B
Point A(x, y)
Point B(x, y)
(3, 2)
Point C(x, y)
(3, 2)
Point D(x, y)
(3, 2)
C
D
33
The Coordinate Plane

• On a piece of grid paper draw lines
  representing the x-axis and the y-axis.

• Graph

Point A(x, y) A(2, 4)
Point B(x, y) B(2, 0)
Point C(x, y) C(2, 3)
Point D(x, y) D(2, 5)
34
The Coordinate Plane

• On a piece of grid paper draw lines
  representing the x-axis and the y-axis.

• Graph

Point A(x, y) A(2, 4)
Point B(x, y) B(2, 0)
Point C(x, y) C(2, 3)
Point D(x, y) D(2, 5)
x 2
1) What do you notice about the graphs of these
points?
35
The Coordinate Plane

• On a piece of grid paper draw lines
  representing the x-axis and the y-axis.

• Graph

Point A(x, y) A(2, 4)
Point B(x, y) B(2, 0)
Point C(x, y) C(2, 3)
Point D(x, y) D(2, 5)
x 2
1) What do you notice about the graphs of these
points?
They lie on a vertical line.
36
The Coordinate Plane

• On a piece of grid paper draw lines
  representing the x-axis and the y-axis.

• Graph

Point A(x, y) A(2, 4)
Point B(x, y) B(2, 0)
Point C(x, y) C(2, 3)
Point D(x, y) D(2, 5)
x 2
1) What do you notice about the graphs of these
points?
They lie on a vertical line.
2) What do you notice about the x-coordinates of
these points?
37
The Coordinate Plane

• On a piece of grid paper draw lines
  representing the x-axis and the y-axis.

• Graph

Point A(x, y) A(2, 4)
Point B(x, y) B(2, 0)
Point C(x, y) C(2, 3)
Point D(x, y) D(2, 5)
x 2
1) What do you notice about the graphs of these
points?
They lie on a vertical line.
2) What do you notice about the x-coordinates of
these points?
They are the same number.
38
The Coordinate Plane

• On a piece of grid paper draw lines
  representing the x-axis and the y-axis.

• Graph

Point A(x, y) A(2, 4)
Point B(x, y) B(2, 0)
Point C(x, y) C(2, 3)
Point D(x, y) D(2, 5)
Write a general statement about ordered pairs
that have the same x-coordinate.
39
The Coordinate Plane

• On a piece of grid paper draw lines
  representing the x-axis and the y-axis.

• Graph

Point A(x, y) A(2, 4)
Point B(x, y) B(2, 0)
Point C(x, y) C(2, 3)
Point D(x, y) D(2, 5)
x 2
Write a general statement about ordered pairs
that have the same x-coordinate.
40
The Coordinate Plane
On the same coordinate plane

• Graph

Point W(x, y) W(4, 4)
Point X(x, y) X(2, 4)
Point Y(x, y) Y(0, 4)
Point Z(x, y) Z(3, 4)
41
The Coordinate Plane
On the same coordinate plane

• Graph

Point W(x, y) W(4, 4)
Point X(x, y) X(2, 4)
Point Y(x, y) Y(0, 4)
Point Z(x, y) Z(3, 4)
42
The Coordinate Plane
On the same coordinate plane

• Graph

Point W(x, y) W(4, 4)
Point X(x, y) X(2, 4)
Point Y(x, y) Y(0, 4)
Point Z(x, y) Z(3, 4)
1) What do you notice about the graphs of these
points?
43
The Coordinate Plane
On the same coordinate plane

• Graph

Point W(x, y) W(4, 4)
Point X(x, y) X(2, 4)
Point Y(x, y) Y(0, 4)
Point Z(x, y) Z(3, 4)
1) What do you notice about the graphs of these
points?
They lie on a horizontal line.
44
The Coordinate Plane
On the same coordinate plane

• Graph

Point W(x, y) W(4, 4)
Point X(x, y) X(2, 4)
Point Y(x, y) Y(0, 4)
Point Z(x, y) Z(3, 4)
1) What do you notice about the graphs of these
points?
They lie on a horizontal line.
2) What do you notice about the y-coordinates of
these points?
45
The Coordinate Plane
On the same coordinate plane

• Graph

Point W(x, y) W(4, 4)
Point X(x, y) X(2, 4)
Point Y(x, y) Y(0, 4)
Point Z(x, y) Z(3, 4)
1) What do you notice about the graphs of these
points?
They lie on a horizontal line.
2) What do you notice about the y-coordinates of
these points?
They are the same number.
46
The Coordinate Plane
On the same coordinate plane

• Graph

Point W(x, y) W(4, 4)
Point X(x, y) X(2, 4)
Point Y(x, y) Y(0, 4)
Point Z(x, y) Z(3, 4)
Write a general statement about ordered pairs
that have the same y-coordinate.
47
The Coordinate Plane
On the same coordinate plane

• Graph

Point W(x, y) W(4, 4)
Point X(x, y) X(2, 4)
Point Y(x, y) Y(0, 4)
Point Z(x, y) Z(3, 4)
y 4
Write a general statement about ordered pairs
that have the same y-coordinate.
48
The Coordinate Plane
Theorem 2 4 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____
49
The Coordinate Plane
Theorem 2 4 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____
x a
y b
50
The Coordinate Plane
Theorem 2 4 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____
x a
y b
Graph the lines x 3
51
The Coordinate Plane
Theorem 2 4 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____
x a
y b
Graph the lines x 3
52
The Coordinate Plane
Theorem 2 4 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____
x a
y b
Graph the lines x 3
y 2
53
The Coordinate Plane
Theorem 2 4 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____
x a
y b
Graph the lines x 3
y 2
54
The Coordinate Plane
Theorem 2 4 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____
x a
y b
Graph the lines x 3
y 2
Graph the point of intersection of theselines.
55
The Coordinate Plane
Theorem 2 4 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____
x a
y b
Graph the lines x 3
y 2
Graph the point of intersection of theselines.
56
The Coordinate Plane
End of Lesson