Name:
Date:
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Unit 3: Systems of Linear Equations Performance Task
Community Park
Your town has decided to build a new community park. Your task is to create a graph that the construction
workers and landscapers will use as a guide.
The community park will sit on a piece of land that measures 150 meters by 200 meters. The x-axis is the
southern border of the property (200 meters long) and the y-axis is the western border of the property (150
meters long).
1) The boundaries for the park are described by these four equations. Graph these four equations to sketch
the diagram of the park. Use the provided tables to calculate the needed points and sketch each line.
2x + 12y = 1800
4x – y = 600
y=0
x=0
2𝑥 + 12𝑦 = 1800
0
150
4𝑥 − 𝑦 = 600
150
175
2) Calculate the solution to this system to find the location of the northeast corner of the park and plot that
point on your diagram:
2x + 12y = 1800
4x – y = 600
Unit 6 Performance Task
CT Algebra I Model Curriculum Version 3.0
Name:
Date:
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3) The developers are not too far along in their planning, but they have decided the placement of the
fenced-in basketball court. The northwest corner of the rectangular basketball court is at the intersection
of the lines 2𝑥 − 5𝑦 = −460 and 2𝑥 + 3𝑦 = 500. Calculate the location of this point algebraically.
4) The court extends 20 meters directly south from the given corner (this is the shorter side of the
basketball court) and 30 meters east. Sketch the perimeter of the basketball court on your park grid.
5) As another requirement of the park design, you must include two pathways that go along the diagonals
of the park (connecting the vertices of the quadrilateral).
a. Identify the coordinates of the four corners of the park. Then use the coordinates of the corners to
calculate the equations of the diagonal lines that model the two pathways. Clearly state which two
points you are using to calculate each diagonal pathway.
Pathway 1:
Pathway 2:
b. Choose a feature (i.e. fountain, rose garden, bench, tree, fish pond, gazebo, etc.) to place at the
intersection of the two pathways and sketch the feature of your choice on the diagram.
Bonus: Use the equations that model each pathway to calculate the coordinates of its exact location.
The developers will get back to you with more details for the community park after the next meeting. Your task
at this point in the planning stage is to create the graph containing the four sides that outline the community
park and include a sketch of the location of the basketball court and the two pathways. They will use this outline
to continue planning.
Unit 6 Performance Task
CT Algebra I Model Curriculum Version 3.0
Name:
Community Park Checklist
Date:
Page 3 of 3
_____ 1) The x-axis and y-axis of the coordinate plane are labeled and appropriate scales are indicated.
_____ 2) The four lines that create the boundaries of the park are correctly graphed and labeled.
_____ 3) The basketball court is correctly placed, labeled, and is in proportion to the given scale of the park
design.
_____ 4) The pathways are correctly placed and labeled and are the correct length given the scale of the
graph. The equations of the two pathways are written and the intersection is labeled with the
coordinate pair.
_____ 5) You have attached work that shows how you solved each system of equations.
_____ 6) You have explained why you chose the method you used to solve each system of equations.
_____ 7) You have used correct spelling, grammar and sentence structure in the written explanations of
your work
Unit 6 Performance Task
CT Algebra I Model Curriculum Version 3.0