Perpendicular means that two lines are at right angles to each other.
Study the diagram carefully as you note each of the following facts.
The number lines are called axes. The horizontal line is the x-axis and the vertical is the y-axis. The zero point at which they are perpendicular is called the origin.
Axes is plural. Axis is singular.
Positive is to the right and up; negative is to the left and down.
The arrows indicate the number lines extend indefinitely. Thus the plane extends indefinitely in all directions.
The plane is divided into four parts called quadrants. These are numbered in a counterclockwise direction starting at the upper right.
Points on the plane are designated by ordered pairs of numbers written in parentheses with a comma between them, such as (5,7). This is called an ordered pair because the order in which the numbers are written is important. The ordered pair (5,7) is not the same as the ordered pair (7,5). Points are located on the plane in the following manner.
First, start at the origin and count left or right the number of spaces designated by the first number of the ordered pair. Second, from the point on the x-axis given by the first number count up or down the number of spaces designated by the second number of the ordered pair. Ordered pairs are always written with x first and then y, (x,y). The numbers represented by x and y are called the coordinates of the point (x,y).
This is important. The first number of the ordered pair always refers to the horizontal direction and the second number always refers to the vertical direction.
Example 1 On the following Cartesian coordinate system the points A (3,4), B (0,5), C (-2,7), D (-4,1), E (-3,-4), F (4,-2), G (0,-5), and H (-6,0) are designated. Check each one to determine how they are located.
