4.17: Points in the Coordinate Plane
Have you ever wanted to find a sunken ship? Take a look at this dilemma.
Gina and Cameron are very excited because they are going to go on a dive to see a sunken ship. The dive is quite shallow which is unusual because most dives are found at depths that are too deep for two junior divers. However, this one is at 40 feet, so the two divers can go to see it.
They have the following map to chart their course. Cameron wants to figure out exactly how far the boat will be from the sunken ship. Each square represents 160 cubic feet of water.
First, he makes a note of the coordinates. Then he can use the map to calculate the distance.
We use coordinate grids like this one all the time. Use the information in this lesson to help Cameron figure out the coordinates of his boat and the sunken ship. Then you will be able to estimate the distance between them.
Guidance
In working with integers in previous Concepts, we used both horizontal (lefttoright) and vertical (upanddown) number lines. Imagine putting a horizontal and a vertical number line together. In doing this, you could create a coordinate plane.
In a coordinate plane like the one shown, the horizontal number line is called the
We can use coordinate planes to represent points, twodimensional geometric figures, or even realworld locations. If you think about a map, you will realize that you see a coordinate plane on a map. Then you use coordinates to find different locations. Let’s look at how we can use a coordinate plane.
How do we name points on a coordinate plane?
Each point on a coordinate plane can be named by an ordered pair of numbers, in the form
 The first number in an ordered pair identifies the
x− coordinate. That coordinate describes the point's position in relation to thex− axis.  The second number in an ordered pair identifies the
y− coordinate. That coordinate describes the point's position in relation to they− axis.
You can remember that the
Write these terms and their definitions in your notebook.
Identifying the coordinates of a point is similar to locating a point on a number line. The main difference is that you need to find the point that corresponds to both of the given coordinates.
Name the ordered pair that represents the location of point
Here are the steps to naming the coordinates.
 To start, place your finger at the origin.
 Then move your finger to the right along the
x− axis until your finger is lined up under pointZ . You will need to move 4 units to the right to do that. Moving to the right along a number line means you are moving in a positive direction. So, thex− coordinate is a positive integer 4.  Now, move your finger up from the
x− axis until your finger reaches pointZ . You will need to move 5 units up to do that. Moving up along they− axis means you are moving in a positive direction. So, they− coordinate is a positive integer 5.
The arrows below show how you should have moved your finger to determine the coordinates.
To name the ordered pair, write the
So, the ordered pair (4, 5) names the location of point
Now that you know how to name points using an ordered pair, it is time learn how to graph them from an ordered pair.
Graphing points on a coordinate plane is similar to naming them. Given an ordered pair, you can move your finger left or right along the
There are a few key points to remember.
 If the
x− coordinate is positive, move to the right of the origin. If thex− coordinate is negative, move to the left.  If the
y− coordinate is positive, move up parallel to they− axis. If they− coordinate is negative, move down.
Here is another one.
Plot the ordered pair (5, 3) as a point on the coordinate plane.
Here are the steps:
 The
x− coordinate is a negative integer, 5, so move your finger 5 units to the left along thex− axis. Your finger should be pointing to the integer 5 on thex− axis.  The
y− coordinate is a positive integer, 3, so move your finger 3 units up from thex− axis.
Plot a point at that location. That point represents the ordered pair (5, 3).
Sometimes, the points you plot on a coordinate grid will form the vertices of a geometric figure, such as a triangle. Try this one on your own.
Example A, B, C
Triangle
Solution: Here are the steps to graphing the triangle.
 To plot vertex
A at (2, 5), start at the origin. Move 2 units to the left and then 6 units down. Plot and label pointA .  To plot vertex
B at (0, 3), start at the origin. Thex− coordinate is zero, so do not move to the left or right. From the origin, simply move 3 units up. Plot and label pointB .  To plot vertex
C at (6, 3), start at the origin. Move 6 units to the right and then 3 units down. Plot and label pointC .
Connect the vertices with line segments to show the sides of the triangle, as shown.
Here is the original problem once again. Use this information to help Cameron with the coordinates and the distance.
Gina and Cameron are very excited because they are going to go on a dive to see a sunken ship. The dive is quite shallow which is unusual because most dives are found at depths that are too deep for two junior divers. However, this one is at 40 feet, so the two divers can go to see it.
They have the following map to chart their course. Cameron wants to figure out exactly how far the boat will be from the sunken ship. Each square represents 160 cubic feet of water.
First, he makes a note of the coordinates. Then he can use the map to calculate the distance.
First, here are the coordinates of each item on the map.
The sunken ship is marked at (4, 8).
The dive boat is marked at (3, 7).
Notice the arrows. Once they get to the sunken ship, Gina and Cameron will swim up 1 unit and over 6 units.
If each unit = 160 sq. feet, then we can multiply
Gina and Cameron will swim through 1120 cubic feet of water from the boat to the sunken ship.
Vocabulary
Here are the vocabulary words in this Concept.
 Coordinate Plane
 a plane with four quadrants where locations are marked according to coordinates.

x− axis  the horizontal line on the coordinate plane

y− axis  the vertical line on the coordinate plane
 Origin
 the point where the \begin{align*}x\end{align*} axis and the \begin{align*}y\end{align*} axis meet
 \begin{align*}x\end{align*}coordinate
 the first coordinate in an ordered pair.
 \begin{align*}y\end{align*}coordinate
 the second coordinate in an ordered pair.
Guided Practice
Here is one for you to try on your own.
This coordinate grid shows locations in Jimmy's city. Name the ordered pair that represents the location of the city park.
Answer
Here are the steps to figuring out the coordinates of the city park.
 Place your finger at the origin.
 Next, move your finger to the right along the \begin{align*}x\end{align*}axis until your finger is lined up above the point representing the city park. You will need to move 2 units to the left to do that. Moving to the left along the \begin{align*}x\end{align*}axis means that you are moving in a negative direction. Your finger will point to a negative integer, 2, so that is the \begin{align*}x\end{align*}coordinate.
 Now, move your finger down from the \begin{align*}x\end{align*}axis until your finger reaches the point for the city park. You will need to move 6 units down to do that. Moving down parallel to the \begin{align*}y\end{align*}axis means that you are moving in a negative direction. Your finger will be aligned with the negative integer, 6, on the \begin{align*}y\end{align*}axis, so, that is the \begin{align*}y\end{align*}coordinate.
The arrows below show how you should have moved your finger to find the coordinates.
So, the ordered pair (2, 6) names the location of the city park.
Video Review
Here is a video for review.
 This is a James Sousa video on ordered pairs and the coordinate plane.
Practice
Directions: Use what you have learned to complete this practice section.
1. Name the ordered pair that represents each of these points on the coordinate plane.
Directions: Below is a map of an amusement park. Name the ordered pair that represents the location of each of these rides.
2. roller coaster
3. Ferris wheel
4. carousel
5. log flume
Directions: Name the ordered pairs that represent the vertices of triangle \begin{align*}FGH\end{align*}.
6. \begin{align*}F\end{align*}
7. \begin{align*}G\end{align*}
8. \begin{align*}H\end{align*}
Directions: Name the ordered pairs that represent the vertices of pentagon \begin{align*}ABCDE\end{align*}.
9. \begin{align*}A\end{align*}
10. \begin{align*}B\end{align*}
11. \begin{align*}C\end{align*}
12. \begin{align*}D\end{align*}
13. \begin{align*}E\end{align*}
14. On the grid below, plot point \begin{align*}V\end{align*} at (6, 4).
15. On the grid below, plot point a triangle with vertices \begin{align*}R (4, 1), \ S (4, 4)\end{align*}, and \begin{align*}T (3, 4)\end{align*}.
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Image Attributions
Here you'll learn to name and graph ordered pairs of integer coordinates in a coordinate plane.