Introduction
Josh wants to show his pen pal where he lives in relation to his school. Josh lives three blocks from his school. In fact, he lives three blocks South of his school. In order to coordinate where Josh lives in relation to his school, Josh has decided to graph the location of his school on a coordinate grid.
Do you know how to do this?
This Concept is about graphing ordered pairs in four quadrants. You will learn how to do this in this Concept.
Guided Learning
Way back in an earlier Concept, you learned how to graph points on a coordinate grid. This coordinate grid only had one quadrant or section to it. This was necessary at the time because you didn’t know about integers yet. Here is a picture of the coordinate grid with only one quadrant.
Now let’s think back to that Concept and review some of the vocabulary associated with coordinate grids and graphing points.
Now if we are going to plot a point on the coordinate grid pictured above, we will have an \begin{align*}x\end{align*} coordinate and a \begin{align*}y\end{align*} coordinate. We go across the \begin{align*}x\end{align*} axis to the \begin{align*}x\end{align*} value and then up to the \begin{align*}y\end{align*} value and that is where we plot the point.
Let’s practice.
Plot (3, 5) on the coordinate grid then label it point \begin{align*}A\end{align*}
Now we have point (3, 5) graphed on the coordinate grid.
But this isn’t the only coordinate grid! Now that you know about integers, we can see all four quadrants of the coordinate grid. While in the past we only graphed points in one quadrant, there are actually FOUR quadrants to the coordinate grid. Let’s take a look.
Here you can see all four quadrants of the coordinate grid. If you look at each axis, you will see that there are positive and negative values on each axis. The \begin{align*}x\end{align*} axis has positive values to the right of the origin, and negative values to the left of the origin. The \begin{align*}y\end{align*} axis has positive values above the origin and negative values below the origin. We can plot points in all four quadrants.
How can we graph points in all four quadrants?
We can work on this in the same way that we did when we had only one quadrant. We use ordered pairs. There will be an \begin{align*}x\end{align*} value and a \begin{align*}y\end{align*} value in the ordered pair. The \begin{align*}x\end{align*} value can be positive or negative and the \begin{align*}y\end{align*} value can be positive or negative. We start at the origin, move to the \begin{align*}x\end{align*} value and then to the \begin{align*}y\end{align*} value. Then we can graph the point.
Graph the point (-4, 3) and name it point \begin{align*}P\end{align*}.
Here we started at the origin. Worked our way to the left to negative four on the \begin{align*}x\end{align*} axis then worked our way up to positive three on the \begin{align*}y\end{align*} axis. That is where we graphed point \begin{align*}P\end{align*}.
Practice Identifying each ordered pair on the Coordinate grid.
Example A, B, C, D
Solution: A = (1,1), B = (-3,-1), C = (0, 4), D = (2, -3)
Here is the original problem once again.
Josh wants to show his pen pal where he lives in relation to his school. Josh lives three blocks from his school. In fact, he lives three blocks south of his school. In order to coordinate where Josh lives in relation to his school, Josh has decided to graph the location of his school on a coordinate grid.
Do you know how to do this?
To accomplish this goal, Josh drew a coordinate grid like this one.
He wants to graph his school three blocks south of his home.
To do this, Josh put his home at the origin which has the coordinates (0,0).
Then if Josh goes three blocks south of his school, we can put it at (0,3).
These are the coordinates of Josh's school.
Practice Set
Here is one for you to try on your own.
Identify the coordinates of the following point. Use an coordinate grid to help you.
Begin at the origin. Move five units to the right of the origin and three units down. Where are you?
Answer
If we begin at the origin, that has the coordinates of (0,0).
We move 5 units to the right on the x axis that is +5.
We move 3 units down, that is -3.
Our answer is (5, -3).
Video Review
Here is a video for review.
Khan Academy, The Coordinate Plane
Directions: Identify the coordinates of each of the points plotted on the coordinate grid.
1. \begin{align*}A\end{align*}
2. \begin{align*}B\end{align*}
3. \begin{align*}C\end{align*}
4. \begin{align*}D\end{align*}
5. \begin{align*}E\end{align*}
6. \begin{align*}F\end{align*}
7. \begin{align*}G\end{align*}
8. \begin{align*}H\end{align*}
9. \begin{align*}I\end{align*}
10. \begin{align*}J\end{align*}
Directions: Answer the following questions.
11. What is the center point called?
12. What are it's coordinates?
13. If you move to the right of the origin, are the values positive or negative?
14. What is the horizontal line called?
15. What is the vertical line called?
Review
- If we are going to plot a point on the coordinate grid we will have an \begin{align*}x\end{align*} coordinate and a \begin{align*}y\end{align*}coordinate. We go across the \begin{align*}x\end{align*} axis to the \begin{align*}x\end{align*} value and then up to the \begin{align*}y\end{align*} value and that is where we plot the point.
- If you look at each axis, you will see that there are positive and negative values on each axis. The \begin{align*}x\end{align*} axis has positive values to the right of the origin, and negative values to the left of the origin. The \begin{align*}y\end{align*} axis has positive values above the origin and negative values below the origin. We can plot points in all four quadrants.
- We can work on this in the same way that we did when we had only one quadrant. We use ordered pairs. There will be an \begin{align*}x\end{align*} value and a \begin{align*}y\end{align*} value in the ordered pair. The \begin{align*}x\end{align*} value can be positive or negative and the \begin{align*}y\end{align*}value can be positive or negative. We start at the origin, move to the \begin{align*}x\end{align*} value and then to the \begin{align*}y\end{align*} value. Then we can graph the point.