2.14: Points in the Coordinate Plane
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 yard12 feet directly behind the house.
 The housewhich 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 twodimensional 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 \begin{align*}x\end{align*}
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 \begin{align*}x\end{align*}
(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 \begin{align*}x\end{align*}
(3, 4)
This ordered pair has two values. It has an \begin{align*}x\end{align*}
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 \begin{align*}x\end{align*}
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 \begin{align*}x\end{align*}
Notice that this point is actually on the \begin{align*}y\end{align*}
Now let's practice.
Example A
A = _____
Solution: (3,2)
Example B
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 \begin{align*}x\end{align*}
x and \begin{align*}y\end{align*}y values that tell us where an object is located.
 Origin

where the \begin{align*}x\end{align*}
x and \begin{align*}y\end{align*}y axis meet, has a value of (0, 0)

\begin{align*}x\end{align*}
x axis  the horizontal line of a coordinate grid

\begin{align*}y\end{align*}
y axis  the vertical line of a coordinate grid
 Ordered pair

\begin{align*}(x, y)\end{align*}
(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.
Answer
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.
James Sousa, Plotting Points on the Coordinate Plane
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)
axis
The axis is the horizontal axis in the coordinate plane, commonly representing the value of the input or independent variable.axis
The axis is the vertical number line of the Cartesian plane.Abscissa
The abscissa is the coordinate of the ordered pair that represents a plotted point on a Cartesian plane. For the point (3, 7), 3 is the abscissa.Cartesian Plane
The Cartesian plane is a grid formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin.Coordinate grid
The coordinate grid is formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin. The coordinate grid is also called a Cartesian Plane or coordinate plane.Coordinate Plane
The coordinate plane is a grid formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin. The coordinate plane is also called a Cartesian Plane.Coordinates
The coordinates of a point represent the point's location on the Cartesian plane. Coordinates are written in ordered pairs: .Ordered Pair
An ordered pair, , describes the location of a point on a coordinate grid.Ordinate
The ordinate is the coordinate of the ordered pair that represents a plotted point on a Cartesian plane. For the point (3, 7), 7 is the ordinate.Origin
The origin is the point of intersection of the and axes on the Cartesian plane. The coordinates of the origin are (0, 0).Image Attributions
Here you'll learn how to graph given points on a coordinate grid.
Concept Nodes:
axis
The axis is the horizontal axis in the coordinate plane, commonly representing the value of the input or independent variable.axis
The axis is the vertical number line of the Cartesian plane.Abscissa
The abscissa is the coordinate of the ordered pair that represents a plotted point on a Cartesian plane. For the point (3, 7), 3 is the abscissa.Cartesian Plane
The Cartesian plane is a grid formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin.Coordinate grid
The coordinate grid is formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin. The coordinate grid is also called a Cartesian Plane or coordinate plane.Coordinate Plane
The coordinate plane is a grid formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin. The coordinate plane is also called a Cartesian Plane.Coordinates
The coordinates of a point represent the point's location on the Cartesian plane. Coordinates are written in ordered pairs: .Ordered Pair
An ordered pair, , describes the location of a point on a coordinate grid.Ordinate
The ordinate is the coordinate of the ordered pair that represents a plotted point on a Cartesian plane. For the point (3, 7), 7 is the ordinate.Origin
The origin is the point of intersection of the and axes on the Cartesian plane. The coordinates of the origin are (0, 0).