To find the perimeter of the rectangle given its vertices at coordinates (2,1), (2,3), (4,4), and (4,2), we first need to clarify the positions of these points and identify the lengths of the sides.
- Identifying the vertices:
- (2,1) and (2,3) are both vertical points along the line \(x=2\) with the same x-coordinate but different y-coordinates.
- (4,4) and (4,2) are also both vertical points along the line \(x=4\) with the same x-coordinate but different y-coordinates.
From the coordinates, we can see that:
- The side length between (2,1) and (2,3) (vertical side) is \( 3 - 1 = 2 \).
- The side length between (4,2) and (4,4) (also a vertical side) is \( 4 - 2 = 2 \).
- The horizontal distance between (2,1) and (4,1) is \( 4 - 2 = 2 \).
- The horizontal distance between (2,3) and (4,3) is also \( 4 - 2 = 2 \).
- Calculating the perimeter: The perimeter \(P\) of a rectangle is given by the formula: \[ P = 2 \times (\text{length} + \text{width}) \] In this case, the lengths of the sides are:
- Length (vertical) = 2
- Width (horizontal) = 2
Thus, the perimeter can be calculated as: \[ P = 2 \times (2 + 2) = 2 \times 4 = 8 \]
Since the question asks for rounding to the nearest tenth, the perimeter of the rectangle is: \[ \boxed{8.0} \]
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