Question

Jenna has a garden with coordinate A(2,-1), B(4,3), C(9,3), D(7,-1) where each unit is 1 foot.

Answer 1

Answer:

a) The dimensions of the garden are: 4.5 ft and 5 ft

b) 22.5 ft² of fencing material

c) The most precise name for the shape of the garden is a Rectangle

Step-by-step explanation:

a) Jenna has a garden with coordinate A(2,-1), B(4,3), C(9,3), D(7,-1) where each unit is 1 foot.

What are the dimensions of the garden rounded to the nearest 10th? (Looking for the lengths of the sides)

When we are given coordinates, we find the dimensions using the formula

= √(x2 - x1)² - (y2 - y1)²

(x1 , y1) and (x2 - y2)

For side AB

A(2,-1), B(4,3)

= √(4 - 2)² + (3 - (-1))²

= √2² + 4²

= √4 + 16

= √20 units = √20 feet

= 4.472135955 feet

Approximately = 4.5 feet

For side BC

B(4,3), C(9,3)

= √(9 - 4)² + (3 - 3)²

= √5² + 0²

= √25

= 5 units = 5 feet

For side CD

C(9,3), D(7,-1)

= √(7 - 9)² + (-1 - 3)²

= √(-2)² + -4²

= √4 + 16

= √20 units = √20 feet

= 4.472135955 feet

Approximately = 4.5 feet

For side AD

A(2,-1), D(7,-1)

= √(7 - 2)² + (-1 - (-1))²

= √5² + (-1 + 1)²

= √5² + 0²

= √25

= 5 units = 5 feet

Therefore, the dimensions of the garden are: 4.5ft and 5 ft

b) If Jenna decides to buy fencing for the garden, how much fence material does she need to buy? (Free response)

To buy fencing material for the garden, we have to find the area of the garden

Formula = Length × Width

= 4.5 ft × 5 ft

= 22.5 ft²

Therefore, Jenna needs to buy 22.5 square feet of fencing material.

c) What is the most precise name for the shape of the garden?

From the above calculation, we can see that

Side AB = Side CD = 4.5 ft

Side BC = Side AD = 5 ft

Therefore, the most precise name for the shape of the garden is a Rectangle