**Polygons in the Coordinate Plane**

Common Core Standard - M6G3

**Introduction**

In this lesson you will learn how to:

- draw polygons in the coordinate plan given coordinates for the vertices
- use coordinates to find the length of a side

Below are some important points to remember prior to beginning our lesson.

- The coordinate plane is made up of the x-axis (a horizontal line) and y-axis (a vertical line).
- The coordinate plane has four quadrants.
- An ordered pair is a set of two numbers that represent the x and y coordinate.

Complete the activity below to test your knowledge of the coordinate plane.

If you need further instruction please visit this web page before moving to the next page.

__Using Coordinates to Draw Polygons__

Now that you know how to graph we can easily take those skills and graph multiple points to create shapes. The graph below has four point that are plotted onto the coordinate plane. The points are then connected with lines to form a rectangle.

You can then determine the distance around the rectangle (or the perimeter). This concept can then be connected to the real world by figuring out the perimeter needed. .

For example, suppose the rectangle in the above coordinate plane represents a garden. You are trying to figure out how fence is needed to protect your garden. If you count the length of each side you can then determine how much fence you need to purchase. In the example above you will need 22 feet of fence (assuming each space on the coordinate plane represents 1 foot) to protect your garden.

Example Number 2

Suppose you are wanting to hang a picture frame in your room. You are trying to determine the perimeter of the picture frame that is needed. We'll plot this on a coordinate plane to get a better understanding of the length needed. Using your own graph paper plot the following points listed below and find the distance around the figure created. Once you have done so enter the total distance below.

**Points to be Plotted**

Point A: (2, -3)

Point B: (2, 2)

Point C: (-3, 2)

Point D: (-3, -3)

If you need graph paper to plot your points visit this website. Or, you can use an online plotter to plot your points.

__Plotting other Designs__

Using the coordinates below create the designs below.

**1. (1, 1), (1, 9), (4, 9), (4, 6), (6, 6), (6, 9), (9, 9), (9, 1), (6, 1), (6, 4), (4, 4), (4, 1), (1, 1)**

**2. (-1, 1), (-1, 6), (-3, 4), (-8, 9), (-9, 8), (-4, 3), (-6, 1), (-1, 1)**

**3. (5, -1), (7, -6), (6, -6), (6, -9), (4, -9), (4, -6), (3, -6), (5, -1)**

**4. (-2, -1), (-5, -4), (-8, -1), (-9, -2), (-6, -5), (-9, -8), (-8, -9), (-5, -6), (-2, -9), (-1, -8), (-4, -5), (-1,-2), (-2, -1)**

__Challenge-Create Your Own!__

1. First, use a piece of graph paper or create your own coordinate plane.

2. Next, draw out your design.

3. After you have finished creating your own design, list the points used to create your design.

4. Shared with a friend or classmate and have him/her plot your design!