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Apply the techniques of using the coordinates to find the length and the width of the polygon. Use the length and the width to...Asked by goofy ah bugger
Apply the techniques of using the coordinates to find the length and the width of the polygon. Use the length and the width to find the perimeter of the polygon in miles. Rectangle ABCD has vertices point A (1,−3) , point B (5, −3) , point C (5, −1) , and point D (1, −1) .(1 point)
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GPT-4o
To find the perimeter of the rectangle ABCD with given vertices, you first need to determine the lengths of its sides using the coordinates. Here's a step-by-step approach:
1. **Identify the coordinates of the vertices:**
- Point \( A (1, -3) \)
- Point \( B (5, -3) \)
- Point \( C (5, -1) \)
- Point \( D (1, -1) \)
2. **Calculate the lengths of the sides:**
- Side \( AB \) (which is the same as \( CD \))
- Side \( BC \) (which is the same as \( DA \))
**To find the length of \( AB \):**
The coordinates for \( AB \) are \( A (1, -3) \) and \( B (5, -3) \).
Using the distance formula for horizontal line segments (since y-coordinates are the same):
\[ \text{Length of } AB = |x_2 - x_1| \]
\[ = |5 - 1| \]
\[ = 4 \]
So, \( AB = 4 \) units.
**To find the length of \( BC \):**
The coordinates for \( BC \) are \( B (5, -3) \) and \( C (5, -1) \).
Using the distance formula for vertical line segments (since x-coordinates are the same):
\[ \text{Length of } BC = |y_2 - y_1| \]
\[ = |-1 - (-3)| \]
\[ = |-1 + 3| \]
\[ = 2 \]
So, \( BC = 2 \) units.
Since it's a rectangle, the opposite sides are equal:
- \( AB = CD = 4 \) units
- \( BC = DA = 2 \) units
3. **Calculate the perimeter of the rectangle:**
The perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (\text{Length} + \text{Width}) \]
\[ P = 2 \times (4 + 2) \]
\[ P = 2 \times 6 \]
\[ P = 12 \text{ units} \]
Therefore, the perimeter of the rectangle ABCD is 12 units. If you need this in miles, you need to convert the units appropriately (assuming the units are given in miles, then the perimeter is simply 12 miles).
1. **Identify the coordinates of the vertices:**
- Point \( A (1, -3) \)
- Point \( B (5, -3) \)
- Point \( C (5, -1) \)
- Point \( D (1, -1) \)
2. **Calculate the lengths of the sides:**
- Side \( AB \) (which is the same as \( CD \))
- Side \( BC \) (which is the same as \( DA \))
**To find the length of \( AB \):**
The coordinates for \( AB \) are \( A (1, -3) \) and \( B (5, -3) \).
Using the distance formula for horizontal line segments (since y-coordinates are the same):
\[ \text{Length of } AB = |x_2 - x_1| \]
\[ = |5 - 1| \]
\[ = 4 \]
So, \( AB = 4 \) units.
**To find the length of \( BC \):**
The coordinates for \( BC \) are \( B (5, -3) \) and \( C (5, -1) \).
Using the distance formula for vertical line segments (since x-coordinates are the same):
\[ \text{Length of } BC = |y_2 - y_1| \]
\[ = |-1 - (-3)| \]
\[ = |-1 + 3| \]
\[ = 2 \]
So, \( BC = 2 \) units.
Since it's a rectangle, the opposite sides are equal:
- \( AB = CD = 4 \) units
- \( BC = DA = 2 \) units
3. **Calculate the perimeter of the rectangle:**
The perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (\text{Length} + \text{Width}) \]
\[ P = 2 \times (4 + 2) \]
\[ P = 2 \times 6 \]
\[ P = 12 \text{ units} \]
Therefore, the perimeter of the rectangle ABCD is 12 units. If you need this in miles, you need to convert the units appropriately (assuming the units are given in miles, then the perimeter is simply 12 miles).
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