What is the perimeter of rectangle WXYZ, with vertices W Left-parenthesis negative 3 comma 7 right-parenthesis, X Left-parenthesis negative 5 comma 4 right-parenthesis, Y Left-parenthesis 1 comma 0 right-parenthesis, and Z Left-parenthesis 3 comma 3 right-parenthesis, to the nearest unit?
(1 point)
Responses
36 units
36 units
30 units
30 units
22 units
22 units
11 units
To find the perimeter of a rectangle, we need to add up the lengths of all four sides.
The distance between W and X is 3 - (-5) = 8 units.
The distance between X and Y is 0 - 4 = 4 units.
The distance between Y and Z is 3 - 1 = 2 units.
The distance between Z and W is 7 - 3 = 4 units.
So, the perimeter of rectangle WXYZ is 8 + 4 + 2 + 4 = 18 units.
Therefore, the nearest unit for the perimeter of rectangle WXYZ is 18 units.
To find the perimeter of rectangle WXYZ, you need to calculate the sum of the lengths of its four sides.
The length of side WX can be found using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2).
Using points W(-3, 7) and X(-5, 4), we have √((-5 + 3)^2 + (4 - 7)^2) = √(4 + 9) = √13.
The length of side XY can be found using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2).
Using points X(-5, 4) and Y(1, 0), we have √((1 + 5)^2 + (0 - 4)^2) = √(36 + 16) = √52 = 2√13.
The length of side YZ can be found using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2).
Using points Y(1, 0) and Z(3, 3), we have √((3 - 1)^2 + (3 - 0)^2) = √(4 + 9) = √13.
The length of side ZW can be found using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2).
Using points Z(3, 3) and W(-3, 7), we have √((-3 - 3)^2 + (7 - 3)^2) = √(36 + 16) = √52 = 2√13.
Now, we can calculate the perimeter by adding the lengths of all the sides: √13 + 2√13 + √13 + 2√13 = 6√13.
To the nearest unit, the perimeter of rectangle WXYZ is approximately 22 units.