Find the perimeter of rectangle ABCD , with vertices A(1,7) , B(4,7) , C(4,−4) , and D(1,−4) .
To find the perimeter of the rectangle, we need to calculate the distance between each pair of adjacent vertices and then sum them up.
Let's calculate the distance between each pair of adjacent vertices:
1. Distance between points A(1,7) and B(4,7):
d1 = √[(4-1)² + (7-7)²]
= √[3² + 0²]
= √9
= 3
2. Distance between points B(4,7) and C(4,-4):
d2 = √[(4-4)² + (-4-7)²]
= √[0² + (-11)²]
= √121
= 11
3. Distance between points C(4,-4) and D(1,-4):
d3 = √[(1-4)² + (-4+4)²]
= √[(-3)² + 0²]
= √9
= 3
4. Distance between points D(1,-4) and A(1,7):
d4 = √[(1-1)² + (7+4)²]
= √[0² + 11²]
= √121
= 11
Now, let's sum up the distances to find the perimeter:
Perimeter = d1 + d2 + d3 + d4
= 3 + 11 + 3 + 11
= 28
Therefore, the perimeter of rectangle ABCD is 28 units.
Find the perimeter of rectangle EFGH , with vertices E(6,9) and F(4,9) , G(4,−5) , and H(6,−5) .
To find the perimeter of the rectangle, we need to calculate the distance between each pair of adjacent vertices and then sum them up.
Let's calculate the distance between each pair of adjacent vertices:
1. Distance between points E(6,9) and F(4,9):
\(d_1 = \sqrt{(4-6)^2 + (9-9)^2} = \sqrt{(-2)^2 + 0^2} = \sqrt{4} = 2\)
2. Distance between points F(4,9) and G(4,-5):
\(d_2 = \sqrt{(4-4)^2 + (-5-9)^2} = \sqrt{0^2 + (-14)^2} = \sqrt{196} = 14\)
3. Distance between points G(4,-5) and H(6,-5):
\(d_3 = \sqrt{(6-4)^2 + (-5+5)^2} = \sqrt{2^2 + 0^2} = \sqrt{4} = 2\)
4. Distance between points H(6,-5) and E(6,9):
\(d_4 = \sqrt{(6-6)^2 + (9+5)^2} = \sqrt{0^2 + 14^2} = \sqrt{196} = 14\)
Now, let's sum up the distances to find the perimeter:
Perimeter = \(d_1 + d_2 + d_3 + d_4\)
Perimeter = \(2 + 14 + 2 + 14\)
Perimeter = 32
Therefore, the perimeter of rectangle EFGH is 32 units.
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.
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?
To find the perimeter of the house, we need to calculate the distance between each pair of adjacent vertices and then sum them up.
Let's calculate the distance between each pair of adjacent vertices:
1. Distance between points A(6,12) and B(6,-6):
\(d_1 = \sqrt{(6-6)^2 + (-6-12)^2} = \sqrt{0^2 + (-18)^2} = \sqrt{324} = 18\)
2. Distance between points B(6,-6) and C(-4,-6):
\(d_2 = \sqrt{(-4-6)^2 + (-6+6)^2} = \sqrt{(-10)^2 + 0^2} = \sqrt{100} = 10\)
3. Distance between points C(-4,-6) and D(-4,12):
\(d_3 = \sqrt{(-4+4)^2 + (12+6)^2} = \sqrt{0^2 + 18^2} = \sqrt{324} = 18\)
4. Distance between points D(-4,12) and A(6,12):
\(d_4 = \sqrt{(6+4)^2 + (12-12)^2} = \sqrt{10^2 + 0^2} = \sqrt{100} = 10\)
Now, let's sum up the distances to find the perimeter:
Perimeter = \(d_1 + d_2 + d_3 + d_4\)
Perimeter = \(18 + 10 + 18 + 10\)
Perimeter = 56
Therefore, the perimeter of the outside of the house is 56 yards.
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.
To find the perimeter of the backyard, we need to calculate the distance between each pair of adjacent vertices and then sum them up.
Let's calculate the distance between each pair of adjacent vertices:
1. Distance between points A(-11,10) and B(-1,10):
\(d_1 = \sqrt{(-1+11)^2 + (10-10)^2} = \sqrt{10^2 + 0^2} = \sqrt{100} = 10\)
2. Distance between points B(-1,10) and C (-1,-10):
\(d_2 = \sqrt{(-1+1)^2 + (-10-10)^2} = \sqrt{0^2 + (-20)^2} = \sqrt{400} = 20\)
3. Distance between points C (-1,-10) and D (-11,-10):
\(d_3 = \sqrt{(-11+1)^2 + (-10+10)^2} = \sqrt{(-10)^2 + 0^2} = \sqrt{100} = 10\)
4. Distance between points D (-11,-10) and A(-11,10):
\(d_4 = \sqrt{(-11+11)^2 + (10+10)^2} = \sqrt{0^2 + 20^2} = \sqrt{400} = 20\)
Now, let's sum up the distances to find the perimeter:
Perimeter = \(d_1 + d_2 + d_3 + d_4\)
Perimeter = 10 + 20 + 10 + 20
Perimeter = 60
Therefore, the perimeter of the backyard is 60 feet.
To find the perimeter of the quilt, we need to calculate the distance between each pair of adjacent vertices and then sum them up.
Let's calculate the distance between each pair of adjacent vertices:
1. Distance between points A(1,4) and B(1,-1):
\(d_1 = \sqrt{(1-1)^2 + (-1-4)^2} = \sqrt{0^2 + (-5)^2} = \sqrt{25} = 5\)
2. Distance between points B(1,-1) and C(-3,-1):
\(d_2 = \sqrt{(-3-1)^2 + (-1+1)^2} = \sqrt{(-4)^2 + 0^2} = \sqrt{16} = 4\)
3. Distance between points C(-3,-1) and D(-1,4):
\(d_3 = \sqrt{(-1+3)^2 + (4+1)^2} = \sqrt{2^2 + 5^2} = \sqrt{4+25} = \sqrt{29}\)
4. Distance between points D(-1,4) and A(1,4):
\(d_4 = \sqrt{(1+1)^2 + (4-4)^2} = \sqrt{2^2 + 0^2} = \sqrt{4} = 2\)
Now, let's sum up the distances to find the perimeter:
Perimeter = \(d_1 + d_2 + d_3 + d_4\)
Perimeter = \(5 + 4 + \sqrt{29} + 2\)
Perimeter ≈ 16.08
Therefore, William will need approximately 16.08 feet of thread to stitch the quilt to the backing.