Transcript Chapter 2 Section 2

Chapter 2 Section 2
The Coordinate Plane
Coordinate System
The point at
which the
number lines
intersect is
called the
origin.
The plane
that contains
the x- and yaxis is called
the
coordinate
plane.
The vertical
number line
is called the
y-axis.
The
horizontal
number line
is called the
x-axis.
Ordered Pair
In mathematics an ordered pair of numbers is
used to locate any point on a coordinate
plane.
• The first number in an ordered pair is called
the x-coordinate. It corresponds to a number
on the x-axis.
• The second number is called the y-coordinate.
It corresponds to a number on the y-axis.
x-coordinate
(1, 5)
y-coordinate
Y
7
6
(1, 5)
5
4
3
2
1
-7
-6
-5
-4 -3
-2
-1
-1
-2
-3
-4
-5
-6
-7
1
2
3
4
5
6
7
X
Example 1
This is the origin.
(0, 0)
Write an ordered pair that names each point.
Start with the origin.
Move left on the xaxis to find the xcoordinate of the first
point . The xcoordinate is -2.
(-2, 4)
Move up along the
grid lines to find the
y-coordinate. The ycoordinate is 4.
The next coordinate x
is 4 and y is -1. (4, -1)
Your Turn
Write an ordered pair that names each point.
A (3, 2)
(-4, 0)
D
C
B
(3, -3)
(-1, -3)
• A point can be named by both a letter and its
ordered pair. For example, P (2, 3) means
point P has an x-coordinate of 2 and a ycoordinate of 3.
• To graph an ordered pair on a coordinate
plane, draw a dot at the point that
corresponds to the ordered pair. This is called
plotting the point.
Example 2
Graph P(2, 3) on a coordinate plane.
•
•
•
•
Start at the origin, (0, 0).
The x-coordinate is 2. So, move 2 units to the right.
The y-coordinate is 3. So, move 3 units up and draw a dot.
Label the dot with the letter P.
Example 3
Graph Q (-3, 0) on a coordinate plane.
• Start at the origin, (0, 0).
• The x-coordinate is -3. So, move 3 units to the left.
• The y-coordinate is 0. So, the dot is placed on the axis.
Your Turn
Graph each point on the coordinate plane.
R (2, -4)
S (-1, 4)
T (0, -3)
S
T
R
• The x-axis and y-axis separate the coordinate
plane into four regions, called quadrants. The
quadrants are numbered as shown at the
below. Note that the axes are not located in
any of the quadrants.
Quadrant II
(-, +)
Quadrant I
(+, +)
Quadrant III
(-, -)
Quadrant IV
(+, -)
Example 4
Name the quadrant in which each point is
located.
A (5, -4)
The x-coordinate is positive, and the ycoordinate is negative. So, point A is located
in Quadrant IV.
Example 5
Name the quadrant in which each point is
located.
B (2, 0)
Point B lies on the x-axis. It is not located in a
quadrant.
Your Turn
Name the quadrant in which each point is
located.
C (-2, 7)
D(-4, 9)
E (0, -3)
C = Quadrant III
D = Quadrant II
E = none
You can use ordered pairs to show
how data are related.
• Dolphins can swim at 30 mph over long distances. Then, 30x represents
the total distance traveled. Evaluate the expression to find the distances
traveled in 1, 2, and 3 hours. The graph the ordered pairs (time, distance).
Distance
(miles)
x
30x
1
30
2
60
3
90
100
90
80
70
60
50
40
30
20
10
0
Distance
(mi)
Time (hours)
1
2
3
Hours
4