High School

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On a coordinate plane, WXYZ is a square. Segment WZ is one side of the square and has endpoints W (-8,-5) and Z (-4,-2). What is the perimeter, in units, of WXYZ?

Answer :

The perimeter of square WXYZ is calculated using the distance between points W and Z with coordinates (-8,-5) and (-4,-2) respectively. The length of one side is found to be 5 units, leading to a total perimeter of 20 units.

The question is asking for the perimeter of a square given two endpoints of one side of the square (WZ) on a coordinate plane. To find the perimeter, we first need to calculate the length of the side WZ. The endpoints given are W (-8,-5) and Z (-4,-2), and the distance formula is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates.

So, the calculation is as follows:

  1. Calculate the difference in x-coordinates: (-4) - (-8) = 4
  2. Calculate the difference in y-coordinates: (-2) - (-5) = 3
  3. Calculate the length of WZ: sqrt((4)^2 + (3)^2) = sqrt(16 + 9) = sqrt(25) = 5 units
  4. Since WXYZ is a square, all sides have the same length, so the perimeter is 4 times the length of one side: 4 * 5 = 20 units

Thus, the perimeter of square WXYZ is 20 units.

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