Ask a New Question
Menu

(Perimeter and Area on the Coordinate Plane MC)

A home has a rectangular kitchen. If listed as ordered pairs, the corners of the kitchen are (7, 6), (−4, 6), (7, −9), and (−4, −9). What is the area of the kitchen in square feet?

9 ft2
52 ft2
121 ft2
165 ft2
Question 3(Multiple Choice Worth 2 points)
(Perimeter and Area on the Coordinate Plane MC)

The vertices of a rectangle are plotted.

A graph with both the x and y axes starting at negative 8, with tick marks every one unit up to 8. The points negative 5 comma 2, 4 comma 2, negative 5 comma negative 4, and 4 comma negative 4 are each labeled.

What is the area of the rectangle?

15 square units
30 square units
45 square units
54 square units
Question 4(Multiple Choice Worth 2 points)
(Perimeter and Area on the Coordinate Plane MC)

The vertices of a rectangle are plotted.

A graph with both the x and y axes starting at negative 7, with tick marks every one unit up to 7. The points negative 3 comma 4, 2 comma 4, negative 3 comma negative 4, and 2 comma negative 4 are each labeled.

What is the perimeter of the rectangle?

40 units
26 units
8 units
5 units
Question 5(Multiple Choice Worth 2 points)
(Perimeter and Area on the Coordinate Plane MC)

Which of the following points is the fourth vertex needed to create a rectangle with vertices located at (−29, 11), (−4, −2), and (−29, −2)?

(−29, −11)
(−29, 2)
(−4, 11)
(−4, 2)
Question 6(Multiple Choice Worth 2 points)
(Perimeter and Area on the Coordinate Plane MC)

A gardener would like to add to their existing garden to make more flowers available for the butterflies that visit the garden. Her current garden is 45 square feet. If she added another rectangular piece with vertices located at (−21, 7), (−23, 7), (−21, 12), and (−23, 12), what is the total area of the garden?

10 ft2
55 ft2
225 ft2
450 ft2
Question 7(Multiple Choice Worth 2 points)
(Perimeter and Area on the Coordinate Plane MC)

A student has a rectangular bedroom. If listed as ordered pairs, the corners of the bedroom are (18, 25), (18, −11), (−19, 25), and (−19, −11). What is the perimeter in feet?

73 feet
146 feet
36 feet
37 feet

1 answer

Let's go through each question one by one:

Question 1:

The vertices of the kitchen are:

  • (7, 6)
  • (−4, 6)
  • (7, −9)
  • (−4, −9)

To find the area of the rectangle:

  1. Calculate the length: \( |7 - (-4)| = 7 + 4 = 11 \) ft
  2. Calculate the width: \( |6 - (-9)| = 6 + 9 = 15 \) ft
  3. Area = Length × Width = \( 11 \times 15 = 165 \) ft²

Answer: 165 ft²

Question 2:

The vertices of the rectangle are:

  • (−5, 2)
  • (4, 2)
  • (−5, −4)
  • (4, −4)

To find the area of the rectangle:

  1. Calculate the length: \( |4 - (-5)| = 4 + 5 = 9 \) units
  2. Calculate the width: \( |2 - (-4)| = 2 + 4 = 6 \) units
  3. Area = Length × Width = \( 9 \times 6 = 54 \) square units

Answer: 54 square units

Question 3:

The vertices of the rectangle are:

  • (−3, 4)
  • (2, 4)
  • (−3, −4)
  • (2, −4)

To find the perimeter of the rectangle:

  1. Calculate the length: \( |2 - (-3)| = 2 + 3 = 5 \) units
  2. Calculate the width: \( |4 - (-4)| = 4 + 4 = 8 \) units
  3. Perimeter = 2 × (Length + Width) = \( 2 \times (5 + 8) = 2 \times 13 = 26 \) units

Answer: 26 units

Question 4:

Given vertices are:

  • (−29, 11)
  • (−4, −2)
  • (−29, −2)

The missing vertex must share the x-coordinate with (−4, −2) and the y-coordinate with (−29, 11). Thus, the fourth vertex is (−4, 11).

Answer: (−4, 11)

Question 5:

The area of the additional rectangular piece is found using the vertices:

  • (−21, 7)
  • (−23, 7)
  • (−21, 12)
  • (−23, 12)

To find its area:

  1. Calculate the length: \( |-21 - (-23)| = 2 \) units
  2. Calculate the width: \( |12 - 7| = 5 \) units
  3. Area of the additional piece = Length × Width = \( 2 \times 5 = 10 \) ft²

Total area of the garden = Current area + New area = \( 45 + 10 = 55 \) ft²

Answer: 55 ft²

Question 6:

The vertices of the bedroom are:

  • (18, 25)
  • (18, −11)
  • (-19, 25)
  • (-19, -11)

To find the perimeter:

  1. Calculate the length: \( |18 - (-19)| = 18 + 19 = 37 \) feet
  2. Calculate the width: \( |25 - (-11)| = 25 + 11 = 36 \) feet
  3. Perimeter = 2 × (Length + Width) = \( 2 \times (37 + 36) = 2 \times 73 = 146 \) feet

Answer: 146 feet

In summary:

  • Question 1: 165 ft²
  • Question 2: 54 square units
  • Question 3: 26 units
  • Question 4: (−4, 11)
  • Question 5: 55 ft²
  • Question 6: 146 feet