11.15: Polygon Classification in the Coordinate Plane
Remember Josh from the last Concept?
Well, Josh created a different map to send to his pen pal in New Zealand. On his map, he placed four different things. He placed his home, the skatepark, the library and his friend Sarah's house.
Here are the coordinates of Josh's map.
Home (3,1)
Skatepark (3,5)
Library (2,5)
Sarah's house (2,1)
Josh plotted these points on a coordinate grid and then drew lines connecting the points.
What shape figure united these points?
Do you know?
This Concept is about graphing geometric figures given coordinates of vertices. You will be able to identify the figure created on Josh's map by the end of the Concept.
Guidance
Now that you have learned how to graph points in all four quadrants, you can look at graphing lines and figures on the coordinate grid. If you have the coordinates of each vertex of a figure, you can easily graph it on the coordinate grid. Remember that the coordinates are the ordered pairs of each point. The coordinates let you know where to graph each point.
Graph a figure with the coordinates \begin{align*}A(4,3) \ B(2,3) \ C(2, 1) \ D(4,1)\end{align*}
To start with, we plot each point on the coordinate grid and then we connect the lines. This will give us a geometric figure.
Now that we have it graphed, you can use what you have already learned about geometric figures to name the figure.
This is a rectangle.
You can graph any geometric figure on the coordinate grid as long as you have been given the coordinates.
First, plot each point.
Then, connect the points to form a figure.
Finally, use what you have learned to name the figure drawn.
Let’s practice one more.
Graph and name the following figure with these coordinates \begin{align*}D(1,3) \ E(5,3) \ F(7,1) \ G(1,1)\end{align*}
Here we have graphed a four sided figure with one pair of parallel sides. This is a trapezoid.
Now it's time for you to try a few on your own. Graph each figure and then name the figure.
Example A
\begin{align*}(0,2)(2,0)(0,3)\end{align*}
Solution: Triangle
Example B
\begin{align*}(1,3)(5,3)(7,1)(1,1)\end{align*}
Solution: Trapezoid
Example C
\begin{align*}(3,3)(0,3)(0,0)(3,0)\end{align*}
Solution: Square
Here is the original problem once again.
Well, Josh created a different map to send to his pen pal in New Zealand. On his map, he placed four different things. He placed his home, the skatepark, the library and his friend Sarah's house.
Here are the coordinates of Josh's map.
Home (3,1)
Skatepark (3,5)
Library (2,5)
Sarah's house (2,1)
Josh plotted these points on a coordinate grid and then drew lines connecting the points.
What shape figure united these points?
Do you know?
When you plot these points on the coordinate grid and connect the lines, you will see that a rectangle is the shape formed by the lines and points.
This is our answer.
Vocabulary
Here are the vocabulary words in this Concept.
 Quadrants
 the four sections of a coordinate grid
 Origin

the place where the \begin{align*}x\end{align*}
x and \begin{align*}y\end{align*}y axis’ meet at (0, 0)
 Ordered Pair

the \begin{align*}x\end{align*}
x and \begin{align*}y\end{align*}y values used to locate points on a coordinate grid \begin{align*}(x,y)\end{align*}(x,y)

\begin{align*}x\end{align*}
x axis  the horizontal axis on the coordinate grid

\begin{align*}y\end{align*}
y axis  the vertical axis on the coordinate grid
 Coordinates

the \begin{align*}x\end{align*}
x and \begin{align*}y\end{align*}y values of an ordered pair
Guided Practice
Here is one for you to try on your own.
What is the name of the figure created by graphing the following vertices?
(4,6)
(4,6)
(0,6)
(0,6)
Answer
If you graph all four of these points and connect the vertices, then you will see that there is a trapezoid that is created on the coordinate grid.
Video Review
Here is a video for review.
James Sousa, Plotting Points on the Coordinate Plane
Practice
Directions: Graph each figure using the vertices. Then name the graphed figure.
1.
\begin{align*}&A(2, 2)\\
&B(2, 2)\\
&C(2, 2)\\
&D(2, 2)\end{align*}
2.
\begin{align*}&D(4, 3)\\
&E(1, 1)\\
&F (4, 1)\end{align*}
3. \begin{align*}(1,1)(2,3)(4,1)\end{align*}
4. \begin{align*}(1,3)(5,3)(1,0)(5,0)\end{align*}
5. \begin{align*}(0,5)(3,5)(0,9)(3,9)\end{align*}
6. \begin{align*}(0,6)(2,6)(0,10)(2,10)\end{align*}
7. \begin{align*}(3,6)(6,0)(9,0)\end{align*}
8. \begin{align*}(1,6)(1,8)(9,6)(9,8)\end{align*}
9. \begin{align*}(0,8)(1,5)(5,5)(4,8)\end{align*}
10. \begin{align*}(12,0)(12,6)(7,0)\end{align*}
Directions: For 11  15 Draw five of your own figures on a coordinate grid. Write out each set of coordinates and work with a partner to identify each figure using only the coordinates.
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Term  Definition 

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. 
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. 
Origin  The origin is the point of intersection of the and axes on the Cartesian plane. The coordinates of the origin are (0, 0). 
Quadrants  A quadrant is onefourth of the coordinate plane. The four quadrants are numbered using Roman Numerals I, II, III, and IV, starting in the topright, and increasing counterclockwise. 
Image Attributions
Here you'll learn to graph geometric figures given coordinates of vertices.