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Algebra: Unit 8

Last updated 9 months ago
8 questions
Unit 8 – Item 1
Ronald and Lucy wanted to see how far apart they were in their dorm rooms. They created a
map with a grid where each grid represents a mile. They marked Ronald at (2,1) and Lucy at
(6,4).
1

To the nearest mile, how far apart are they?

1

What set of coordinates would be a midpoint between their two locations?

Unit 8 – Item 2
Both Hank and his sister leave the house going to two different places. Their house is 3 blocks east and then 2 blocks south from his house to the movie theater and 5 blocks west then 3 blocks north from the skating rink.


1

What is the total distance they walked once they reached the theatre and rink? Round your answer to the nearest mile.

1

Who walked farther and by what distance?

Unit 8 – Item 3
A city is planning to design a new park, which will include a rectangular playground, a triangular garden, and a walkway that is perpendicular to one of the playground's sides. The playground's location and dimensions, as well as the garden's vertices, are provided on a coordinate plane.

Use the graph and information below as needed to answer the following questions.
Playground:
• Coordinates of one corner: (2,3)
• Length along the x-axis: 6 units
• Width along the y-axis: 4 units

Triangular Garden:
• Vertices: A(8,2), B(10,6), C(12,2)

Walkway:
• The walkway starts at (8,2) and extends to the line segment BC, going through the
garden and being perpendicular to BC.
1

Calculate the slope of the line segment BC in the garden. Determine the equation of the line perpendicular to this segment that passes through the point (8,2).

1

Determine the amount of fence needed for the garden by calculating the perimeter. Round to the nearest hundredth.

1

How much larger is the playground than the garden? Explain.

Unit 8 - Item 4
David is planning a garden in his backyard, and he wants to incorporate various features in the space. He's using mathematical concepts to plan the layout efficiently. David wants to create a garden path that connects two points in his backyard. He needs to determine the length of the path.
1

Calculate the distance between the starting point (2, 5) and the ending point (8, 10).