Question

A cube 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.

Answer 1

Answer:

  (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).

Answer 2

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

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• The x-coordinates at the top are given by: -3 and 5.
• The y-coordinates at the top are given by: -5 and 3.
• The z-coordinates at the top are given by: 2 and 2.
• The x and y coordinates of the center are the mean of the x and y coordinates of the points at the top.
• The z-coordinate of the center is half of the edge length.

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• Finding the distance of two of the points, we get the edge length, thus:

$D = \sqrt{(-3 - (-3))^2 + (-5 - 3)^2 + (2-2)^2} = \sqrt{8^2} = 8$

• Thus, $z_c = \frac{8}{2} = 4$, and the coordinates of the center are $(x_c, y_c, 4)$

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The coordinates of x and y at the center are:

$x_c = \frac{-3 + 5}{2} = \frac{2}{2} = 1$

$y_c = \frac{-5 + 3}{2} = \frac{-2}{2} = -1$

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

A similar problem is given at https://brainly.com/question/24352869