The **Cartesian plane** consists of two directed
lines that perpendicularly intersect their respective zero points.
The **horizontal** directed
line is called the *x*-axis and the **vertical** directed line is called the *y*-axis.
The point of intersection of the *x*-axis and the *y*-axis is
called the **origin **and** **is denoted by the letter *O*.
The Coordinates
The position of any point on the Cartesian plane is described by using
two numbers: (*x*,* y*). The first number, *x*,
is the horizontal position of the point from the origin. It is called
the *x*-coordinate. The second number, *y*, is the vertical
position of the point from the origin. It is called the *y*-coordinate.
Since a specific order is used to represent the coordinates, they are
called **ordered pairs**.
For example, the ordered pair (5, 8) represents a point 5 units to the
right of the origin in the direction of the *x*-axis and 8 units above the
origin in the direction of the *y*-axis as shown in the diagram
below.
###### We say that:
The *x*-coordinate of point *P* is 5; and the *y*-coordinate
of point *P* is 8.
###### Or simply, we can say that:
The coordinates of point *P* are (5, 8).
Note the following:
- For the point
*P*(5, 8), the ordered pair is (5, 8). So:
5 is the *x*-coordinate, and
8 is the *y*-coordinate.
*P*(5, 8) means *P* is 5 units to the right of and 8 units
above the
origin.
Example 1
State the coordinates of each of the points shown on the Cartesian plane:
Solution:
*A* is 3 units to the right of and 2 units above the origin. So,
point *A* is (3, 2).
B is 5 units to the right of and 5 units above the origin. So,
point *B* is (5, 5).
C is 7 units to the right of and 8 units above the origin. So,
point *C* is (7, 8).
D is 6 units to the left of and 4 units above the origin. So,
point *D* is (–6, 4).
E is 3 units to the left of and 7 units above the origin. So,
point *E* is (–3, 7).
F is 4 units to the left of and 6 units below the origin. So,
point *F* is (–4, –6).
G is 8 units to the left of and 8 units below the origin. So,
point *G* is (–8, –8).
P is 9 units to the right of and 9 units below the origin. So,
point *P* is (9, –9).
Q is 6 units to the right of and 5 units below the origin. So,
point *Q* is (6, –5).
Key Terms
Cartesian plane, *x*-axis, *y*-axis, origin, coordinates, point, *x*-coordinate, *y*-coordinate, ordered
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