# Finding the Side Length of a Polygon in a Coordinate Plane: 6th Grade Lesson

Students will find the length of a side of a polygon drawn in a coordinate plane.

**Introduction: **Determine the side length of a polygon in a coordinate plane, when the points of the side have the same first coordinate or the same second coordinate.

**Lesson Objective:** The lesson is aligned to the Common Core State Standards for Mathematics – 6.G.3 Geometry – 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.

**Materials Required: **Coordinate grids on** **graph paper

## Lesson Procedure:

**Finding the Side Lengths of Polygons in a Coordinate Plane**

- On your graph paper, draw a rectangle with the vertices at the following coordinates:

Point A: (-2, 3)

Point B: (2, 3)

Point C: (2, -2)

Point D: (-2, -2)

To find the length of the sides, count the squares between each vertex. What are the measurements of the length and the width of the rectangle?

**Answers:**

- There are 4 squares between Point A and Point B. There are 5 squares between Point B and Point C. The measurements of the length is 4 units and the width is 5 units.

## Individual or Group Work:

**1. **On a coordinate grid, draw a rectangle with the vertices at the following coordinates:

Point A: (0, 4)

Point B: (3, 4)

Point C: (0, -1)

Point D: (3, -1)

To find the length of the sides, count the squares between each vertex. What are the measurements of the length and the width of the rectangle?

**2. **On a coordinate grid, graph the following city buildings at the following coordinates:

Library: (-2, 4)

Post Office: (5, 4)

School: (5, -3)

Fire Station: (-2, -3)

Each unit on the coordinate grid represents one mile. What is the shortest distance between the Library and the Post Office? What is the shortest distance between the Post Office and the School?

**3. **Audrey is drawing a rectangle on a coordinate grid. She graphed Point A at ( -1, 2 ), Point B at (2, 2), and Point C at ( 2, -2). Where should she graph Point D? What are the measurements of the length and the width of the rectangle?

**4. **Jack is graphing his home and the home of his friend on a coordinate grid. He graphed his home at (0, 0). He graphed Jasper’s home at (9, 0). Each unit on the coordinate grid represents one mile. What is the distance between Jack’s and Jasper’s homes?

**5. **Reese is graphing his home and the home of his cousin on a coordiante grid. He graphed his home at (1, 1). His cousin’s home is 10 miles from Reese. What are the coordinates where Reese could graph his cousin’s home?

## Answers:

**1. **It takes 8 x 4 x 15 cubes, or 480 cubes with side lengths of ¼ inch. The volume of the right rectangular prism is 480/64 = 7 ½ cubic inches or 2 x 1 x 3 ¾ = 7 ½ cubic inches.

**2. **It takes 3 x 1 x 8 cubes, or 24 cubes with side lengths of ½ inch. The volume of the right rectangular prism is 24/8 = 3 cubic inches or 1 ½ x ½ x 4 = 3 cubic inches.

**3. **It takes 9 x 3 x 4 cubes, or 108 cubes with side lengths of ½ inch. The volume of the right rectangular prism is 108/8 = 13 ½ cubic inches or 4 ½ x 1 1/2 x 2 = 13 1/2 cubic inches.

**4. **It takes 3 x 2 x 8 cubes, or 48 cubes with side lengths of ¼ inch. The volume of the right rectangular prism is 48/64 = ¾ cubic inches or ¾ x ½ x 2 = ¾ cubic inches.

**5. **It takes 5 x 7 x 8 cubes, or 280 cubes with side lengths of ½ inch. The volume of the right rectnagular prism is 280/8 = 35 cubic inches or 2 ½ x 3 ½ x 4 = 35 cubic inches.

## Download

**Download the Individual or Group Work here.**

Students should be able to find the volume of right rectangular prism with fractional edge lengths by filling the prisms with unit cubes of the appropriate unit fraction edge lengths and apply the formula *V* = *l w h*.** **