The position of a point on a **Cartesian plane** is represented by
referring to it in terms of a **horizontal line** and a **vertical line**,
which are called the *x*-axis and *y*-axis respectively. The point of intersection of the *x*-axis and the *y*-axis
is called the **origin**.
Often, we draw a set of axes on graph paper as shown below.
The position of any point on the Cartesian plane is described by using
two numbers, (*x*,* y*), that are called **coordinates**. 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, an ordered pair (4, 5) represents a point 4 units to the
right of the origin in the direction
of the *x*-axis, and 5 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 4; and the *y*-coordinate
of point *P* is 5.
###### Or simply, we can say that:
The coordinates of point *P* are (4, 5).
Note the following:
- For the point
*P*(4, 5), the ordered pair is (4, 5). So:
4 is the *x*-coordinate, and
5 is the *y*-coordinate.
*P*(4, 5) means *P* is 4 units to the right of and 5 units
above the origin.
Example 3
State the coordinates of each of the points shown on the Cartesian plane:
##### Solution:
*A* is 1 unit to the right of and 2 units above the origin. So, point *A* is (1, 2).
B is 2 units to the right of and 3 units above the origin. So, point *B* is (2, 3).
C is 2 units to the right of and 4 units above the origin. So, point *C* is (2, 4).
D is 3 units to the right of and 4 units above the origin. So, point *D* is (3, 4).
E is 5 units to the right of and 2 units above the origin. So, point *E* is (5, 2).
F is 7 units to the right of and 3 units above the origin. So, point *F* is (7, 3).
G is 4 units to the right of and 5 units above the origin. So, point *G* is (4, 5).
H is 5 units to the right of and 6 units above the origin. So, point *H* is (5, 6).
I is 1 unit to the right of and 7 units above the origin. So, point *I* is (1, 7).
J is 7 units to the right of and 7 units above the origin. So, point *J* is (7, 7).
Key Terms
point, Cartesian plane, horizontal line, *x*-axis, vertical line, *y*-axis, origin, axes, *x*-coordinate, *y*-coordinate, coordinates, ordered pairs, vertical
position, horizontal position |