Videos, solutions, and lessons to help Grade 6 students learn how to draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Common Core: 6.G.3

__Suggested Learning Targets__

Common Core for Grade 6, More Lessons for Grade 6

**Draw polygons in a plane given coordinates for the vertices and find the length of a side (6.G.3)**

Examples:

1. The vertices of a quadrilateral are A(2,4), B(3,9), C(&,8) and D(8,1). Draw the quadrilateral in a coordinate plane.

2. The vertices of a rectangle are F(1,6), G(7,6), H(&,2) and J(1,2). Draw the rectangle in a coordinate plane and find its perimeter.

**6th Grade: Polygons on the Coordinate Plane**

Part 1: Find the Perimeter

You can use the coordinates of a figure to find its dimensions by finding the distance between two points. To find the distance between two points with the same x-coordinates, subtract their y-coordinates. To find the distance between two points with the same y-coordinates, subtract their x-coordinates.

Examples:

a) A rectangle has vertices A(2,8), B(7,8), C(7,5) and D(2,5). Use the coordinates to find the length of each side. Then find the perimeter of the rectangle.

b) The coordinates of the vertices of a garden are (0,1), (0,4), (8,4) and (8,1). If each unit represents 1.2 inches, find the perimeter in inches of the garden.

c) Each grid square on the zoo map has a length of 200 feet. Find the total distance in feet, around the zoo.

Part 2: Find the area

You can find the area of a figure that has been drawn on a grid paper or graphed on the coordinate plane. Figures can be separated into smaller figures that we know how to find the area of.

a) Find the area of the figure in square units

b) A figure has vertices A(2,5), B(2,6) and C(5,8). Graph the figure and classify it. Then, find the area in square units.

c) Find the area, in square units, of the figure below.

**How to draw polygons and find distances in the coordinate plane?**

You can use ordered pairs to represent vertices of polygons. To draw a polygon in a coordinate plane, plot and connect the ordered pairs.

Example 1: Drawing a polygon in a coordinate plane

The vertices of a quadrilateral are A(2,4), B(3,9), C(7,8) and D(8,1). Draw the quadrilateral in a coordinate plane.

Example 2: Finding a perimeter

The vertices of a rectangle are F(1,6), G(7,6), H(7,2) and J(1,2). Draw the rectangle in a coordinate plane and find its perimeter.

Example 3: Real-life application

In a grid of the exhibition at a zoo, the vertices of the giraffe exhibit are E(0,90), F(60,90), G(100,30), and H(0,30). The coordinates are measured in feet. What is the area of the giraffe exhibit?

**Plotting shapes in all Four Quadrants - 6.G.3**

In this video, students will learn to plot five sided shapes using all four quadrants of the coordinate grid. This video relates to Common Core Standard 6.G.3.

Example:

Plot the points (-4,3), (4,-3), (-4,-1), (4,-1), (0,6)

**Constructing polygon on the coordinate plane example**

Example:

Use the line segments below to create a quadrilateral with vertices at the following points:

(0,9), (0,-7), (8,-7), (8,0)

**Parallelogram on the coordinate plane**

You are graphing polygon ABCD in the coordinate plane. The length of the segment AB must be the same as the length of segment DC, and both segments are horizontal segments. The following are three of the vertices of the polygon: A(1,1), C(4.5,4) and D(-1.5,4)

What are the coordinates of point B, if point B must be in quadrant 1?

Activities:

The following activities are obtained from the Howard County Public School System.

1) The following points were plotted on the coordinate plane:

Point A (-7, 6) Point B (3, 6) Point C (3, -6) Point D (?)

If the distance between Point C and Point B is equal to the distance between Point A and Point D, what are the coordinates for Point D? How do you know?

2) Triangle*PQR *and triangle *QRS *have vertices

*P*(–9,7), *Q*(4,7), *R*(4,–3), and *S*(10,–3).

What is the area, in square units, of quadrilateral*PQSR, *which is formed by the two triangles?

3) Donnie created a triangle on a coordinate plane using coordinates (2,3); (2, 5); (7, 3).

Stewart created a triangle on the same coordinate plane using coordinates (-4, 5); (-4, 7); (-9, 5).

Do their triangles have the same area? Explain why.

Common Core: 6.G.3

- I can draw polygons on a coordinate plane.
- I can solve real world problems with polygons on a coordinate plane.
- I can draw polygons in the coordinate plane.
- I can use coordinates (with the same x-coordinate or the same y-coordinate) to find the length of a side of a polygon.
- I can apply the technique of using coordinates to find the length of a side of a polygon drawn in the coordinate plane to solve real-world and mathematical problems.

Common Core for Grade 6, More Lessons for Grade 6

Examples:

1. The vertices of a quadrilateral are A(2,4), B(3,9), C(&,8) and D(8,1). Draw the quadrilateral in a coordinate plane.

2. The vertices of a rectangle are F(1,6), G(7,6), H(&,2) and J(1,2). Draw the rectangle in a coordinate plane and find its perimeter.

Part 1: Find the Perimeter

You can use the coordinates of a figure to find its dimensions by finding the distance between two points. To find the distance between two points with the same x-coordinates, subtract their y-coordinates. To find the distance between two points with the same y-coordinates, subtract their x-coordinates.

Examples:

a) A rectangle has vertices A(2,8), B(7,8), C(7,5) and D(2,5). Use the coordinates to find the length of each side. Then find the perimeter of the rectangle.

b) The coordinates of the vertices of a garden are (0,1), (0,4), (8,4) and (8,1). If each unit represents 1.2 inches, find the perimeter in inches of the garden.

c) Each grid square on the zoo map has a length of 200 feet. Find the total distance in feet, around the zoo.

Part 2: Find the area

You can find the area of a figure that has been drawn on a grid paper or graphed on the coordinate plane. Figures can be separated into smaller figures that we know how to find the area of.

a) Find the area of the figure in square units

b) A figure has vertices A(2,5), B(2,6) and C(5,8). Graph the figure and classify it. Then, find the area in square units.

c) Find the area, in square units, of the figure below.

You can use ordered pairs to represent vertices of polygons. To draw a polygon in a coordinate plane, plot and connect the ordered pairs.

Example 1: Drawing a polygon in a coordinate plane

The vertices of a quadrilateral are A(2,4), B(3,9), C(7,8) and D(8,1). Draw the quadrilateral in a coordinate plane.

Example 2: Finding a perimeter

The vertices of a rectangle are F(1,6), G(7,6), H(7,2) and J(1,2). Draw the rectangle in a coordinate plane and find its perimeter.

Example 3: Real-life application

In a grid of the exhibition at a zoo, the vertices of the giraffe exhibit are E(0,90), F(60,90), G(100,30), and H(0,30). The coordinates are measured in feet. What is the area of the giraffe exhibit?

In this video, students will learn to plot five sided shapes using all four quadrants of the coordinate grid. This video relates to Common Core Standard 6.G.3.

Example:

Plot the points (-4,3), (4,-3), (-4,-1), (4,-1), (0,6)

Example:

Use the line segments below to create a quadrilateral with vertices at the following points:

(0,9), (0,-7), (8,-7), (8,0)

You are graphing polygon ABCD in the coordinate plane. The length of the segment AB must be the same as the length of segment DC, and both segments are horizontal segments. The following are three of the vertices of the polygon: A(1,1), C(4.5,4) and D(-1.5,4)

What are the coordinates of point B, if point B must be in quadrant 1?

Activities:

The following activities are obtained from the Howard County Public School System.

1) The following points were plotted on the coordinate plane:

Point A (-7, 6) Point B (3, 6) Point C (3, -6) Point D (?)

If the distance between Point C and Point B is equal to the distance between Point A and Point D, what are the coordinates for Point D? How do you know?

2) Triangle

What is the area, in square units, of quadrilateral

3) Donnie created a triangle on a coordinate plane using coordinates (2,3); (2, 5); (7, 3).

Stewart created a triangle on the same coordinate plane using coordinates (-4, 5); (-4, 7); (-9, 5).

Do their triangles have the same area? Explain why.

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