# Illustrative Mathematics Unit 6.7, Lesson 15: Let’s use the coordinate plane to solve problems and puzzles.

Learning Targets:

• I can find the lengths of horizontal and vertical segments in the coordinate plane.
• I can plot polygons on the coordinate plane when I have the coordinates for the vertices.

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Illustrative Math

#### Lesson 15: Let’s use the coordinate plane to solve problems and puzzles.

Let’s use the coordinate plane to solve problems and puzzles.

Illustrative Math Unit 6.7, Lesson 15 (printable worksheets)

#### Lesson 15 Summary

The following diagram shows hos to calculate the perimeter of a polygon in the coordinate plane. #### Lesson 15.1 Figuring Out The Coordinate Plane

Plot points in your assigned quadrant and label them with their coordinates.
Show Coordinate Plane

1. Draw a figure in the coordinate plane with at least three of following properties:
• 6 vertices
• 1 pair of parallel sides
• At least 1 right angle
• 2 sides the same length
1. Is your figure a polygon? Explain how you know.

Scroll down the page for the solutions to the “Are you ready for more?” section.

#### Lesson 15.2 Plotting Polygons

1. Here are the coordinates for four polygons. Move the slider to choose the polygon you want to plot. Move the points, in order, to their locations on the coordinate plane. Sketch each one before changing the slider. Polygon 1: (7,4), (-8,5), (-8,6), (-7,7), (-5,7), (-5,5), (-7,4) Polygon 2: (4,3), (3,3), (2,2), (2,1), (3,0), (4,0), (5,1), (5,2), (4,3) Polygon 3: (-8,-5), (-8,-8), (-5,-8), (-5,-5), (-8,-5) Polygon 4: (-5,1), (-3,-3), (-1,-2), (0,3), (-3,3), (-5,1)
Show Coordinate Plane

#### Are you ready for more?

Find the area of Polygon 4 in this activity. #### Lesson 15.3 Four Quadrants of A-Maze-ing

1. The following diagram shows Andre’s route through a maze. He started from the lower right entrance.
a. What are the coordinates of the first two and the last two points of his route?
b. How far did he walk from his starting point to his ending point? Show how you know.
2. Jada went into the maze and stopped at (-7,2).
Show Maze
a. Plot that point and other points that would lead her out of the maze (through the exit on the upper left side).
b. How far from (-7,2) must she walk to exit the maze? Show how you know.

#### Lesson 15 Practice Problems

1. The coordinates of a rectangle are (3,0), (3,-5), (-4,0) and (-4,-5)
a. What is the length and width of this rectangle?
b. What is the perimeter of the rectangle?
c. What is the area of the rectangle?
2. Draw a square with one vertex on (-3,5) and a perimeter of 20.
3. a. Plot and connect the following points to form a polygon.
(-3,2),(2,2),(2,-4),(-1,-4),(-1,-2),(-3,-2),(-3,2)
b. Find the perimeter of the polygon.
4. For each situation, select all the equations that represent it. Choose one equation and solve it.
a. Jada’s cat weighs 3.45 kg. Andre’s cat weighs 1.2 kg more than Jada’s cat. How much does Andre’s cat weigh?
x = 2.45 + 1.2
x = 3.45 - 1.2
x + 1.2 = 3.45
x - 1.2 = 3.45
b. Apples cost \$1.60 per pound at the farmer’s market. They cost 1.5 times as much at the grocery store. How much do the apples cost per pound at the grocery store?
y = (1.5) · (1.60)
y = 1.60 ÷ 1.5
(1.5)y = 1.60
y/1.5 = 1.60

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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