Polygons on the Coordinate Grid

Introduction
  • I can draw polygons in the coordinate plane given coordinate for the vertices.
  • I can name coordinates the define the polygon with specific properties. 
Task

Task

The vertices of eight polygons are given below. For each polygon:

  • Plot the points in the coordinate plane connect the points in the order that they are listed.

  • Color the shape the indicated color and identify the type of polygon it is.

  • Find the area.

Process

Process I: Watch Video

Process II: 

Polygons on the Coordinate Grid

ü  I can draw polygons in the coordinate plane given coordinate for the vertices.

ü  I can name coordinates the define the polygon with specific properties.

Task

The vertices of eight polygons are given below. For each polygon:

  • Plot the points in the coordinate plane connect the points in the order that they are listed.
  • Color the shape the indicated color and identify the type of polygon it is.
  • Find the area.

 

1.The first polygon is GREY and has these vertices: (−7,4)(−8,5)(−8,6)(−7,7)(−5,7)(−5,5)(−7,4)



2.The second polygon is ORANGE and has these vertices: (−2,−7)(−1,−4)(3,−1)(6,−7)(−2,−7)



3.The third polygon is GREEN and has these vertices: (4,3)(3,3)(2,2)(2,1)(3,0)(4,0)(5,1)(5,2)(4,3)



4.The fourth polygon is BROWN and has these vertices: (0,−10)(0,−8)(7,−10)(0,−10)



5.The fifth polygon is PURPLE and has these vertices: (−8,−5)(−8,−8)(−5,−8)(−5,−5)(−8,−5)



6.The sixth polygon is PINK and has these vertices: (9,−1)(6,1)(6,−3)(9,−1)



7.The seventh polygon is BLUE and has these vertices: (−6,−4)(−6,1)(−9,1)(−9,−4)(−6,−4)



8.The eighth polygon is YELLOW and has these vertices: (−5,1)(−3,−3)(−1,−2)(0,3)(−3,3)(−5,1)


 

 Process III: Word Problems

 

1. If the points on the coordinate plane below are the three vertices of a rectangle . . .
(a) What are the coordinates of the fourth vertex? How do you know?
(b) What are the length and the width of the rectangle?
(c) What are the area and perimeter of the rectangle?
 

2. On a map, the theater is located at (-4,-4), the courthouse is located at (2, 9), and the train station is located at (2,-4). Represent the locations as points on a coordinate grid with a unit of 1 km.
(a) What is the distance from the the theater to the train station? The distance from the train station to the courthouse? How do you know?
(b) What shape does connecting the three locations form?
(c) The mayor is planning on constructing a public plaza in this area. What is the area of the planned plaza?

 

3. The sides of a rectangle in the coordinate plane are parallel to the axes. Two of the vertices of the rectangle are  and . Find coordinates for the other two vertices. Find the area of the rectangle.