Question

Question 1 A)Find the perimeter of rectangle ABCD, with vertices A(1,7), B(4,7), C(4,−4), and D(1,−4).(1 point) $$ units Question 2 A)Find the perimeter of rectangle EFGH, with vertices E(6,9) and F(4,9), G(4,−5), and H(6,−5).(1 point) $$ units Question 3 A)William is getting ready to enter his quilt into a competition at the state fair. Before he enters the quilt, he needs to stitch the top of the quilt to the backing. He created a map of the quilt with the coordinates A(1,4), B(1,−1), C(−3,−1), and D(−1,4). Each unit on the coordinate plane represents 1 foot. Find the perimeter of the quilt in order to determine how much thread William will need to stitch the quilt to the backing.(1 point) $$ feet Question 4 A)A contractor is building a new house. She creates a map with the coordinates A(6,12), B(6,−6), C(−4,−6), and D(−4,12). Each unit on the coordinate plane represents 1 yard. What is the perimeter of the outside of the house?(1 point) $$ yards Question 5 A)A student wants to find the perimeter of their backyard. The student creates a map of their backyard with following coordinates A(−11,10), B(−1,10), C(−1,−10), and D(−11,10). Each unit on the coordinate plane represents 1 foot. Solve to find the perimeter.(1 point) $$ feet

Answer 1

[AI-generated answer — Bot GPT 3.5]

Question 1 A)We will use the distance formula to find the lengths of each side of the rectangle.

Side AB: √((4-1)^2 + (7-7)^2) = √3^2 + 0^2 = 3 units
Side BC: √((4-4)^2 + (-4-7)^2) = √0^2 + 11^2 = 11 units
Side CD: √((1-1)^2 + (-4-7)^2) = √0^2 + 11^2 = 11 units
Side DA: √((1-1)^2 + (7-(-4))^2) = √0^2 + 11^2 = 11 units

Perimeter = 3 + 11 + 11 + 11 = 36 units

Answer: The perimeter of rectangle ABCD is 36 units.

Question 2 A)We will use the distance formula to find the lengths of each side of the rectangle.

Side EF: √((4-6)^2 + (9-9)^2) = √2^2 + 0^2 = 2 units
Side FG: √((4-4)^2 + (-5-9)^2) = √0^2 + 14^2 = 14 units
Side GH: √((6-4)^2 + (-5-(-5))^2) = √2^2 + 0^2 = 2 units
Side HE: √((6-6)^2 + (9-(-5))^2) = √0^2 + 14^2 = 14 units

Perimeter = 2 + 14 + 2 + 14 = 32 units

Answer: The perimeter of rectangle EFGH is 32 units.

Question 3 A)We will use the distance formula to find the lengths of each side of the quilt.

Side AB: √((1-1)^2 + (-1-4)^2) = √0^2 + 5^2 = 5 feet
Side BC: √((-3-1)^2 + (-1-(-1))^2) = √4^2 + 0^2 = 4 feet
Side CD: √((-1-(-3)^2 + (4-(-1))^2) = √2^2 + 5^2 = √4 + 25 = 5.8 (rounded to nearest tenth) feet
Side DA: √((1-(-1)^2 + (4-4)^2) = √2^2 + 0^2 = 2 feet

Perimeter = 5 + 4 + 5.8 + 2 = 16.8 feet

Answer: The perimeter of the quilt is 16.8 feet.

Question 4 A)Using the distance formula to find the lengths of each side of the house.

Side AB: √((6-6)^2 + (-6-12)^2) = √0^2 + 18^2 = 18 yards
Side BC: √((-4-6)^2 + (-6-(-6))^2) = √(-10)^2 + 0^2 = 10 yards
Side CD: √((-4-(-4)^2 + (12-(-6))^2) = √0^2 + 18^2 = 18 yards
Side DA: √((6-(-4)^2 + (12-12)^2) = √10^2 + 0^2 = 10 yards

Perimeter = 18 + 10 + 18 + 10 = 56 yards

Answer: The perimeter of the outside of the house is 56 yards.

Question 5 A)Using the distance formula to find the lengths of each side of the backyard.

Side AB: √((-1-(-11)^2 + (10-10)^2) = √10^2 + 0^2 = 10 feet
Side BC: √((-1-(-1)^2 + (-10-10)^2) = √0^2 + 20^2 = 20 feet
Side CD: √((-11-(-1)^2 + (-10-10)^2) = √10^2 + 0^2 = 10 feet
Side DA: √((-11-(-11)^2 + (10-10)^2) = √0^2 + 0^2 = 0 feet (as it is a single point)

Perimeter = 10 + 20 + 10 + 0 = 40 feet

Answer: The perimeter of the backyard is 40 feet.

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the error. Let me recalculate the perimeters:

Question 1 A)
Using the distance formula to find the lengths of each side:
AB: √((4-1)^2 + (7-7)^2) = √3^2 = 3 units
BC: √((4-4)^2 + (-4-7)^2) = √0^2 + 11^2 = 11 units
CD: √((1-1)^2 + (-4-7)^2) = √0^2 + 11^2 = 11 units
DA: √((1-4)^2 + (7-7)^2) = √3^2 = 3 units

Perimeter = 3 + 11 + 11 + 3 = 28 units

Answer: The perimeter of rectangle ABCD is 28 units.

Question 2 A)
EF: √((4-6)^2 + (9-9)^2) = √2^2 = 2 units
FG: √((4-4)^2 + (-5-9)^2) = √14^2 = 14 units
GH: √((6-4)^2 + (-5-(-5))^2) = √2^2 = 2 units
HE: √((6-6)^2 + (9-(-5))^2) = √14^2 = 14 units

Perimeter = 2 + 14 + 2 + 14 = 32 units

Answer: The perimeter of rectangle EFGH is 32 units.

Question 3 A)
AB: √((1-1)^2 + (-1-4)^2) = √5^2 = 5 units
BC: √((-3-1)^2 + (-1-(-1))^2) = √4^2 = 4 units
CD: √((-1-(-3))^2 + (4-(-1))^2) = √4^2 + 5^2 = √16 + 25 = √41 feet
DA: √((1-(-1))^2 + (4-4)^2) = √2^2 = 2 units

Perimeter = 5 + 4 + √41 + 2 = 11 + √41 feet

Answer: The perimeter of the quilt is 11 + √41 feet.

Question 4 A)
AB: √((6-6)^2 + (-6-12)^2) = √18^2 = 18 yards
BC: √((-4-6)^2 + (-6-(-6))^2) = √10^2 = 10 yards
CD: √((-4-(-4))^2 + (12-(-6))^2) = √18^2 = 18 yards
DA: √((6-(-4))^2 + (12-12)^2) = √10^2 = 10 yards

Perimeter = 18 + 10 + 18 + 10 = 56 yards

Answer: The perimeter of the outside of the house is 56 yards.

Question 5 A)
AB: √((-1-(-11))^2 + (10-10)^2) = √10^2 = 10 feet
BC: √((-1-(-1))^2 + (-10-10)^2) = √20^2 = 20 feet
CD: √((-1-(-11))^2 + (-10-10)^2) = √10^2 = 10 feet
DA: √((-11-(-1))^2 + (10-10)^2) = √10^2 = 10 feet

Perimeter = 10 + 20 + 10 + 10 = 50 feet

Answer: The perimeter of the backyard is 50 feet.

Answer 4

5 is worng

Answer 5

[AI-generated answer — Bot GPT 3.5]

I see the mistake in question 5. Let me recalculate the perimeter:

Question 5 A)
AB: √((-1-(-11))^2 + (10-10)^2) = √10^2 = 10 feet
BC: √((-1-(-1))^2 + (-10-10)^2) = √20^2 = 20 feet
CD: √((-1-(-11))^2 + (-10-10)^2) = √20^2 = 20 feet
DA: √((-11-(-11))^2 + (10-10)^2) = √0^2 = 0 (since it's a single point)

Perimeter = 10 + 20 + 20 = 50 feet

Answer: The correct perimeter of the backyard is 50 feet.

Answer 6

A)Find the perimeter of rectangle ABCD, with vertices A(1,7), B(4,7), C(4,−4), and D(1,−4).(1 point)

Responses

33 units
33 units

28 units
28 units

12 units
12 units

16 units
16 units
Question 2
A)Find the perimeter of rectangle ABCD, with vertices A(−8,3), B(−1,3), C(−1,−6), and D(−8,−6).(1 point)
Responses

30 units
30 units

32 units
32 units

63 units
63 units

36 units
36 units
Question 3
A)Find the perimeter of rectangle LMNO, with vertices L(−2,−1), M(−5,−1), N(−5,−6), and O(−2,−6).(1 point)
Responses

24 units
24 units

15 units
15 units

16 units
16 units

20 units
20 units
Question 4
A)A local park is building a new playground and needs to know how much fencing to buy. The park authority creates a map of the area with the coordinates A(−5,10), B(1,10), C(1,−12), and D(−5,−12). Each unit on the coordinate plane represents 1 yard. Solve to find out how many yards of fencing is needed (the perimeter).(1 point)
Responses

56 yards
56 yards

16 yards
16 yards

12 yards
12 yards

72 yards
72 yards
Question 5
A)A restaurant is building an outside seating area. The owner created a map with the coordinates A(−11,11), B(−3,11), C(−3,1), and D(−11,1). Each unit on the coordinate plane represents 1 foot. Solve to find out how many feet of wall material they will need to build the new area (the perimeter).(1 point)
Responses

52 feet
52 feet

36 feet
36 feet

40 feet
40 feet

80 feet

Answer 7

[AI-generated answer — Bot GPT 3.5]

Question 1:

To find the perimeter of rectangle ABCD, we calculate the distance between each pair of points and sum them up.
AB: √((4-1)^2 + (7-7)^2) = √3^2 = 3 units
BC: √((4-4)^2 + (-4-7)^2) = √0^2 + 11^2 = 11 units
CD: √((1-1)^2 + (-4-7)^2) = √0^2 + 11^2 = 11 units
DA: √((1-4)^2 + (7-7)^2) = √3^2 = 3 units

Perimeter = 3 + 11 + 11 + 3 = 28 units

Therefore, the perimeter of rectangle ABCD is 28 units.

Question 2:
Using the same approach as question 1:
Perimeter = 32 units

Therefore, the perimeter of rectangle ABCD with vertices A(−8,3), B(−1,3), C(−1,−6), and D(−8,−6) is 32 units.

Question 3:
Perimeter = 16 units

Therefore, the perimeter of rectangle LMNO with vertices L(−2,−1), M(−5,−1), N(−5,−6), and O(−2,−6) is 16 units.

Question 4:
Perimeter = 16 yards

Therefore, the park needs 16 yards of fencing for the playground.

Question 5:
Perimeter = 40 feet

Therefore, the restaurant will need 40 feet of wall material to build the new outside seating area.