Rectangle ABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle:
A = (2,−6), B = (5,−6), C = (5,−2), D = (2,−2)
What is the perimeter of rectangle ABCDA, B, C, D?
To find the perimeter of a rectangle, we add up the lengths of all four sides.
Side AB has length 5 - 2 = 3 (just subtract the x-coordinates of A and B, since they lie on the same horizontal line).
Side BC has length -2 -(-6) = 4 (subtract the y-coordinates of B and C, since they lie on the same vertical line).
Side CD has length 5 - 2 = 3 (same as AB).
Side DA has length -2 -(-6) = 4 (same as BC).
Adding all four lengths together, we get:
3 + 4 + 3 + 4 = 14
Therefore, the perimeter of rectangle ABCDA, B, C, D is 14 units.
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To find the perimeter of a rectangle, you need to add up the lengths of all its sides.
Here, we have the vertices of the rectangle as coordinates:
A = (2, -6)
B = (5, -6)
C = (5, -2)
D = (2, -2)
We can visualize this in the coordinate plane:
```
| (5, -2) (C)
--|----- D------C |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
--|----- A------B |
| (2, -6) (A)
```
To calculate the length of each side, we can use the distance formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
For example, to find the length of side AB, we can use points A and B:
Length of AB = √((5 - 2)² + (-6 - (-6))²)
= √(3² + 0²)
= √(9)
= 3
Similarly, we can find the lengths of the other sides:
Length of BC = √((5 - 5)² + (-2 - (-6))²)
= √(0² + 4²)
= √(16)
= 4
Length of CD = √((2 - 5)² + (-2 - (-2))²)
= √((-3)² + 0²)
= √(9)
= 3
Length of DA = √((2 - 2)² + (-6 - (-2))²)
= √(0² + 4²)
= √(16)
= 4
Now, we can add up all the side lengths to find the perimeter:
Perimeter = Length of AB + Length of BC + Length of CD + Length of DA
Perimeter = 3 + 4 + 3 + 4
Perimeter = 14
Therefore, the perimeter of rectangle ABCDA is 14 units.