Acube is located such that its top four corners have the coordinates (−3,−5,2), (−3,3,2), (5,−5,2) and (5,3,2).
give the coordinates of the center of the cube.

The coordinates of the center of the cube are given by: (1,-1,4).

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The coordinates of x and y at the center are:

Thus, the coordinates of the center are: (1,-1,4).

A similar problem is given at link

  (1, -1, -2)

Step-by-step explanation:

The first listed pair of coordinates are adjacent. Their difference is ...

  (-3-(-3), 3-(-5), 2-2) = (0, 8, 0)

indicating the cube has an edge length of 8.

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The second listed pair of coordinates are the ends of a diagonal, so their average will be the center of the given face:

  ((-3+5)/2, (3-5)/2, (2+2)/2) = (1, -1, 2)

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The given points are all in the plane z=2, so the center of the cube will lie in the plane half an edge-length lower: z = 2 -(8/2) = -2.

The center of the cube has coordinates (1, -1, -2).