Positions in two dimensions, such as points on a computer screen or locations on a map require two intersecting number lines, one to show the horizontal location (left and right) and the other to show the vertical location (up and down) as shown below:
Often on a map one of the number lines will be labeled with letters rather than numbers and the other number line will be labeled with positive numbers. Some examples of point location on such a map are shown in the next four examples:
Example 1. Write the letter A at location E3 on the coordinate system which follows:
Answer:
See the coordinate system below.
Example 2. Write the letter B at location C9 on the following coordinate system:
Answer:
See the coordinate system below.
Example 3. What is the location of the triangle?
Answer:
L6
Example 4. What is the location of the circle?
Answer:
C11
The two intersecting number lines are called the coordinate axes, and the two numbers used to locate a point are called the coordinates of the point. The first coordinate gives the horizontal location of the point, while the second number gives the vertical location of the point. The two axes cross at the point (0,0), which is called the origin. Such a system for labeling is called a Cartesian coordinate system. Some examples of this system follow:
Example 5. Place the letter A on the point (-4,2).
Answer:
See picture below.
Example 6. Place the letter B on the point (0,3).
Answer:
See picture below.
Example 7. Place the letter C on the point (-1,-2).
Answer:
See picture below.
Example 8. Place the letter D on the point (3,4).
Answer:
See picture below.
Example 9. Place the letter E on the point (2,-1).
Answer:
See picture below.
Example 10. Place the letter F on the point (-2,0).
Answer:
See picture below.
