# 4.1.3: Ordered Pairs in Four Quadrants

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## Ordered Pairs in Four Quadrants

In this concept, you will learn to graph ordered pairs in four quadrants.

Liam has a crush on Lila. She's a little strange--she has an old school phone booth on her key chain and he suspects that the strange characters that she doodles on her notebook during history class might actually be elvish runes--but he likes her anyway. When Liam asks her to the Spring Fling, it doesn't really surprise him when she responds with a list of coordinates: (-3,5), (3,5), (0,0), (0,-5). Still, he's left wondering whether that's a yes or a no, and he doesn't want to lose face by asking her. How can Liam figure out what this means?

In this concept, you will learn how to graph coordinates in four quadrants.

### Graphing Coordinates in Four Quadrants

A coordinate grid is a grid in which points are graphed. It usually has two or more intersecting lines which divide a plane into quadrants, and in which ordered pairs, or coordinates, are defined. The coordinate grid below has one quadrant, or section, to it.

The origin is the place where the two lines intersect. Its coordinates are defined as (0,0).

The x-axis is the line running from left to right that has the numbers defined on it and is usually labeled with an "x". The x-coordinate of an ordered pair is found with relation to it. All the points located on the x-axis have a y-coordinate of 0.

The y-axis is the central line that runs up-down and is labeled with a "y". Y-coordinates are plotted in reference to this axis. Again, all the x-coordinates of points located on the y-axis are 0.

An ordered pair is a list of two numbers in parenthesis, separated by a comma like this: (5,-3). It tells where a point is located on the coordinate plane. The first number is the x-coordinate. It tells you where to go on the x-axis. If it is positive, you go to the right. If it is negative, you go to the left. The second number is the y-coordinate. It tells you where to go on the y-axis. If it is positive, you go up. If it is negative, you go down.

Here is an example.

Plot (3, 5) on the coordinate grid then label it point A.

First, look at the x-coordinate.

In this case, it is 3. So you go 3 to the right.

Next, look at the y-coordinate.

In this case, it is 5. So you go up 5.

Then, you draw a dot at that place.

Most coordinate grids have four quadrants. They look like this:

Here is an example of a point graphed in a four-quadrant coordinate grid. Graph the point (-4, 3) and name it point P.

First, look at the x-coordinate.

In this case, it is -4. "-" means move to the left, so you go 4 to the left.

Next, look at the y-coordinate.

In this case, it is 3. It is positive, so that means it is up. Go up 3 units.

The result looks like this:

### Examples

Example 4.1.3.1

Earlier, you were given a problem about Liam and his girl troubles.

Lila gave him a list of ordered pairs--(-3,5), (3,5), (0,0), (0,-5)--when he asked her out. Did she say yes or no?

Solution

First, Liam takes some graph paper and jots a coordinate plane.

Next, he sees that one of the points is at the origin, so he draws a dot there.

Then, he moves to the left 3 and up 5 and makes a point there.

Then, he sees that there is another point at 5 on the y-axis, so he goes ahead and moves over to +3 on the x-axis and makes a dot there, opposite the other point. At this point, he has a V and he thinks it could go either way.

Finally, he goes down 5 on the y-axis. There are no other points, so that looks like his answer. Sweet! Now, he just needs to figure out what he's going to wear.

Example 4.1.3.2

Write the coordinates for the following point.

Begin at the origin. Move five units to the right and three units down.

Solution

First, figure out the x-coordinate of the point.

The x-axis is the left-right axis. Right is the positive direction. So, the x-coordinate of the point is 5.

Next, figure out the y-coordinate.

The y-axis is the up-down axis. Down is the negative direction. So, the y-coordinate is -3.

Then, write the ordered pair of the point.

For the following examples, identify each ordered pair on the coordinate grid given.

Example 4.1.3.3

Point A

Solution

First, locate point A.

Next, determine the x-coordinate.

It is at +1 on the x-axis.

Then, determine the y-coordinate.

It is at +1 on the y-axis.

Finally, write the ordered pair.

Example 4.1.3.4

Point B

Solution

First, locate point B.

Next, determine the x-coordinate.

It is at -3 on the x-axis.

Then, determine the y-coordinate.

It is at -1 on the y-axis.

Finally, write the ordered pair.

Example 4.1.3.5

Point C

Solution

First, locate point C.

Next, determine the x-coordinate.

It is on the y-axis without going left or right. That means the x-coordinate is 0.

Then, determine the y-coordinate.

It is at +4 on the y-axis.

Finally, write the ordered pair.

Example 4.1.3.6

Point D

Solution

First, locate point D.

Next, determine the x-coordinate.

It is at +2 on the x-axis.

Then, determine the y-coordinate.

It is at -3 on the y-axis.

Finally, write the ordered pair.

### Review

Identify the coordinates of each of the points plotted on the coordinate grid.

1. A
2. B
3. C
4. D
5. E
6. F
7. G
8. H
9. I
10. J

1. What is the center point called?
2. What are it's coordinates?
3. If you move to the right of the origin, are the values positive or negative?
4. What is the horizontal line called?
5. What is the vertical line called?

### Vocabulary

Term Definition
x−axis The x−axis is the horizontal axis in the coordinate plane, commonly representing the value of the input or independent variable.
y axis The y-axis is the vertical number line of the Cartesian plane.
Ordered Pair An ordered pair, (x,y), describes the location of a point on a coordinate grid.
Origin The origin is the point of intersection of the x and y axes on the Cartesian plane. The coordinates of the origin are (0, 0).
Quadrants A quadrant is one-fourth of the coordinate plane. The four quadrants are numbered using Roman Numerals I, II, III, and IV, starting in the top-right, and increasing counter-clockwise.