Question

A cube is located such that its bottom four corners have the coordinates (−1,−3,−2), (−1,4,−2), (6,−3,−2) and (6,4,−2). Give the coordinates of the center of the cube.

Answer 1

Answer:

The co-ordinates of the center of the cube are (-2.5,0.5,1.5)

Step-by-step explanation:

Since the 'z' co-ordinate of all the points is same hence we can conclude that all the given 4 points are planar.

Thus the problem reduces a planar problem with need to find the center of the square with vertices (-1,-3), (-1,4), (6,-3), (6,4)

Thus the length of the side of the square is$side=\sqrt{(-1+1)^{2}+(4+3)^{2}}\\\\side=\sqrt{(7)^{2}}\\\\\therefore side=7$

The center of the square is given by taking (-1,-3) as reference co-ordinate

(-1+7/2,-3+7/2) = (-2.5,0.5)

Now since center lies above this center of base

Thus the coordinates of the center of the cube are given by (-2.5,0.5,-2+3.5)=(-2.5,0.5,1.5)