Question

Carlos has a garden with coordinates A(3, 0), B(5,5), C(11,5) and D(9,0), where each unit equals one foot.

Part A: Select all of the dimensions of the garden.
A. 6.0 ft
B. 5.4 ft
C. 5.0 ft.
D. 4.5 ft.
E. 11.0 ft.

Part B: If Carlos decides to fence in the garden, how much fencing material should be purchase? Round to the nearest tenth if needed.

Part C: What is the most precise name for the shape of the fence?
A. Parallelogram
B. Rectangle
C. Square
D. Quadrilateral

Answer 1

Answer:

Part A:  A. 6.0 ft; B. 5.4 ft

Part B:  22.8 ft

Part C:  A. Parallelogram

Step-by-step explanation:

Part A

The distance formula for the length between two points (x1, y1) and (x2, y2) is ...

  d = √((x2-x1)^2 +(y2-y1)^2)

For segment AD, the points are A(3, 0) and D(9, 0), so the distance is ...

  AD = √((9-3)^2 +(0-0)^2) = 6

For segment AB, the points are A(3, 0) and B(5, 5), so the distance is ...

  AB = √((5-3)^2 +(5-0)^2) = √29 ≈ 5.3852 ≈ 5.4

A plot of the points reveals the figure to be a parallelogram, so these are the only two dimensions of interest.

Side lengths of the garden fence are 6.0 ft and 5.4 ft.

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Part B

There are two sides of the garden of each length, so the total perimeter length is ...

   P = 2(6.0 +5.4) = 2·11.4 = 22.8 . . . feet

Carlos needs 22.8 feet of fencing material.

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Part C

As we discovered in Part A when we plotted the points, the shape is a parallelogram.

Answer 2

The amount of fencing needed is 22.8 ft. Since the fence has four sides, hence it is a quadrilateral.

The distance between two points A(x₁, y₁) and B(x₂, y₂) is given by:

$AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Given the coordinates A(3, 0), B(5,5), C(11,5) and D(9,0). Hence:

$AB=\sqrt{(5-0)^2+(5-3)^2}=5.4\ ft \\\\\\BC=\sqrt{(5-5)^2+(11-5)^2}=6.0\ ft \\\\\\CD=\sqrt{(11-9)^2+(5-0)^2}=5.4\ ft \\\\\\AD=\sqrt{(0-0)^2+(9-3)^2}=6.0\ ft$

The amount of fencing = AB + BC + CD + AD = 5.4 + 6.0 + 5.4 + 6.0 = 22.8 ft.

Since the fence has four sides, hence it is a quadrilateral.

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