An x-axis and a y-axis
can be combined to form a set of xy-axes, or, as
we'll also often call it, the (x, y) axes. (Note,
singular: axis, plural: axes.) The two axes are perpendicular; that is,
there is an angle of 90 degrees between them. Usually, the x-axis is
horizontal with increasing positive values to the right, and the y-axis is
vertical with increasing positive values upward. The origins of the x- and
y-axes cross at the same point, so, the (x, y) axes has only one origin
shared by both axes.
The (x, y) axes lies on the (x, y) plane. The (x,
y) plane is a flat, two-dimensional surface, extending in these two
dimensions to infinity.
A grid is usually included in drawings of the (x,
y) plane, creating the familiar graph paper look. This grid helps you judge a
point's position relative to either axes.
The (x, y) plane
Points, coordinates and names
The (x, y) axes allows us to locate points on the (x, y) plane using two
numbers. The first number is called the x-coordinate, and it is the location of the point relative
to the x-axis. The second number is called the
y-coordinate. It is the location of the point
relative to the y-axis.
When stating the location of a point using these two numbers, they are
enclosed in parentheses and separated with a comma, as shown in the next
picture.
A point on the (x, y) plane can also have a name, and the name is usually
a single capital letter.
Note in the following picture that relative to the x-axis, the point
lines up 3 units away from the origin toward the right; so, 3 is its
x-coordinate. Also, relative to the y-axis, the point lines up 4 units away
from the origin upward; so, its y-coordinate is 4. The point's location is
therefore stated as: (3, 4).
One point, two coordinates, often a name
The ordered pair and intersecting lines
Again, in the following picture a point has an x-coordinate of 3 and a
y-coordinate of 4. As we have stated, this point's location can be stated as
follows:
(3, 4)
This notation is called an ordered pair. So:
(3, 4) is the ordered pair for a point with
an x-coordinate of 3 and a y-coordinate of 4.
Let's also look at a couple of lines. The first will be a
vertical line that passes through the x-axis at a coordinate
of 3. This vertical line has an equation of x = 3,
and it is shown as a red dashed line in the
following picture. The second line we want to notice is a
horizontal line that passes through a coordinate of 4 on the
y-axis. This horizontal line has an equation of y = 4.
It is shown as a green dashed line in the next
picture. Where these two lines intersect is the spot where our point is
located.
The ordered pair, vertical and horizontal lines
About the following program
What follows is an (x, y) point program that you can control click the
plus and minus buttons in the x- and y-coordinate input sections to change
the values of the coordinates.
This is an EZ Math Movie program. Click the 'Show system' checkbox to
expose the EZ Math Movie programing interface.
An x-axis and a y-axis
can be combined to form a set of xy-axes, or, as
we'll also often call it, the (x, y) axes. (Note,
singular: axis, plural: axes.) The two axes are perpendicular; that is,
there is an angle of 90 degrees between them. Usually, the x-axis is
horizontal with increasing positive values to the right, and the y-axis is
vertical with increasing positive values upward. The origins of the x- and
y-axes cross at the same point, so, the (x, y) axes has only one origin
shared by both axes.
