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# 2.14: Points in the Coordinate Plane

Difficulty Level: Basic Created by: CK-12
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Have you ever tried to make a map using a grid?

Tania and Alex have had a terrific summer. They have harvested many, many vegetables and are now ready to put up a small farm stand in the front of their house. Alex has decided to draw a map of the area and figure out where to put the stand. He likes the idea of using a grid, where 1 box or unit of the grid is equal to 4 feet. That way he can figure out exactly where everything goes. Alex enjoys being organized like that. There are three things that he wishes to put on his grid:

• The garden plot which is in the back yard-12 feet directly behind the house.
• The house-which is 16 feet from Smith St. and 16 feet from Walker St.
• The farm stand

The house is bordered by Smith and Walker streets, so Alex would like to put the farm stand near the corner so that people on both streets will see it. Alex begins drawing his map, but is soon stuck. Here is how far he gets.

Alex needs to figure out how to use the grid so that he can create his map. This will mean that he will need to understand how to plot points on a coordinate grid.

### Guidance

What is a coordinate grid?

A coordinate grid is a graph that allows us to locate points in space. You have probably seen a coordinate grid when you have looked at a map. A map often has letters on one side and numbers on the other side so you can use a letter and a number to locate a city or a specific place. We use a coordinate grid to locate points in two-dimensional space. A pair of numbers, called coordinates , tells us where the point is. We can graph any point in space on the coordinate grid.

What does a coordinate grid look like?

Here is what a coordinate grid looks like.

You can see that this coordinate grid has two lines, one that is vertical and one that is horizontal. It also has one point where the two lines meet. Each of these parts has a special name. Let’s look at naming the parts of a coordinate grid.

What are the names of the parts of a coordinate grid?

To understand this better, let’s look at the diagram. The horizontal axis or the line that goes across is called the $x$ axis . The vertical axis or the line that goes up and down is called the $y$ axis . The point where the two axes meet is called the origin. The origin has the value of (0,0). You can understand the origin a little more if you know about the $x$ and $y$ axis. Every line on the $x$ axis has a different value. The values start at 0 with the origin and go to 17 on the horizontal axis. Each line has a value of 1. Every line on the $y$ axis has a different value. The values start at 0 with the origin and go to 9 on the vertical axis. Each line has a value of 1.

When a point has already been plotted on a coordinate grid, we can use an ordered pair to identify its location. A coordinate is written in the form of an ordered pair. In an ordered pair, there are two numbers put inside a set of parentheses. The first number is an $x$ value and the second number is a $y$ value $(x, y)$ . Let’s look at an ordered pair.

(3, 4)

How do we graph points on a coordinate grid?

To graph a point on the coordinate grid, we use numbers organized as coordinates. A coordinate is written in the form of an ordered pair. In an ordered pair, there are two numbers put inside a set of parentheses. The first number is an $x$ value and the second number is a $y$ value $(x, y)$ . Let’s look at an ordered pair.

(3, 4)

This ordered pair has two values. It has an $x$ value of 3 because the $x$ value comes first. It has a $y$ value of 4. Each ordered pair represents one point on a coordinate grid.

Next, we can graph this ordered pair on the coordinate grid.

We are going to work in one part of the coordinate grid. You will learn about the other sections later.

If we graph (3,4) as one point on the coordinate grid, we start at the origin and count three units on the $x$ axis first. Then working from the 3, we count up four since the $y$ coordinate is four. That is where we put our point.

What about if we have an ordered pair with a 0 in it?

Sometimes, we will have a zero in the ordered pair.

(0, 4)

This means that the $x$ value is zero, so we don’t move along the $x$ axis for our first point. It is zero so we start counting up at zero. The $y$ value is four, so we count up four units from zero.

Notice that this point is actually on the $y$ axis.

Now let's practice.

A = _____

Solution: (3,2)

B = _____

Solution: (4,6)

#### Example C

C = _____

Solution: (7,9)

Now that we have finished the Concept, we can work on helping Tania and Alex. Here is the problem once again.

Tania and Alex have had a terrific summer. They have harvested many, many vegetables and are now ready to put up a small farm stand in the front of their house. Alex has decided to draw a map of the area and figure out where to put the stand. He likes the idea of using a grid, where 1 box or unit of the grid is equal to 4 feet. That way he can figure out exactly where everything goes. Alex enjoys being organized like that.

There are three things that he wishes to put on his grid:

The garden plot, which is in the backyard, 12 feet directly behind the house. The house, which is 16 feet from Smith St. and 16 feet from Walker St. the farm stand

The house is bordered by Smith and Walker streets, so Alex would like to put the farm stand near the corner so that people on both streets will see it. Alex begins drawing his map, but is soon stuck. Here is how far he gets.

### Vocabulary

Here are the vocabulary words in this Concept.

Coordinate grid
a visual way of locating points or objects in space.
Coordinates
the $x$ and $y$ values that tell us where an object is located.
Origin
where the $x$ and $y$ axis meet, has a value of (0, 0)
$x$ axis
the horizontal line of a coordinate grid
$y$ axis
the vertical line of a coordinate grid
Ordered pair
$(x, y)$ the values where a point is located on a grid

### Guided Practice

Here is one for you to try on your own.

Graph (9,3) on the coordinate grid.

To graph this point, we first look at the x value.

The x value is 9. This is the value on the horizontal axis.

Starting at the origin, we count our way across the horizontal axis to the 9.

Then we graph the 3. It is on the y axis.

From 9, we count up three units.

This is where we put our point.

### Video Review

Here is a video for review.

### Practice

Directions: Write the coordinates of each point.

1. A

2. B

3. C

4. D

5. E

6. F

7. G

8. H

9. I

10. J

11. K

12. L

Directions: Graph and label each point on the coordinate grid.

13. M(1, 3)

14. N(2, 4)

15. O(0, 6)

16. P(8, 6)

17. Q(1, 3)

18. R(4, 7)

19. S(7, 7)

20. T(9,0)

21. U(4, 6)

22. V(0, 5)

23. W(6, 8)

24. Y(1, 7)

25. Z(3, 4)

Basic

Oct 29, 2012

Aug 18, 2014