In mathematics, you locate a point on a coordinate system that is similar to a grid. The coordinate system is formed by the intersection of two number lines that meet at right angles at their zero points.
The directions east and north tell you how to
locate a point on a map. 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.
Example
Write the ordered pair that names each point.
1. A
Alternative Solutions :
• Start
at the origin. Move left on the x-axis
to find the x-coordinate of point A. The x-coordinate is –2.
• Move
up along the grid lines to find the y-coordinate.
The y-coordinate is 4.
2. B
Alternative Solutions :
The x-coordinate is 4, and the y-coordinate is –1.
The
ordered pair for point B is (4, –1).
3. C
Alternative Solutions :
Point C is the origin. The ordered pair for
the origin is (0, 0).
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 y-coordinate 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
4. Graph
P(2, 3) on a coordinate plane.
Alternative Solutions :
• Start at the origin, O.
• 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.
Example
5. Graph
Q(–3, 0) on a coordinate plane.
Alternative Solutions :
• Start at the origin, O.
• 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.
The x-axis and the y-axis separate the coordinate
plane into four regions, called
quadrants.
The quadrants are numbered as shown at the right. Note that the axes are not located
in any of the quadrants.
Example
Name the quadrant in which each point is located.
6. A(5, –4)
Alternative Solutions :
The x-coordinate
is positive, and the y coordinate is
negative.
So, point A
is located in Quadrant IV.
7. B(2, 0)
Alternative Solutions :
Point B lies on the x-axis. It is not located in a quadrant.
You can use ordered pairs to show
how data are related.
Example
Biology Link
8. Dolphins can swim
at 30 mph over long distances. Let x represent the number of hours. Then, 30x
represents the total distance traveled. Evaluate the expression to find the
distances traveled in 1, 2, and 3 hours. Then graph the ordered pairs (time,
distance).
Alternative Solutions :
Sumber
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