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If (2, 3, 5) is one end of a diameter of the sphere x² + y² + z² - 6x - 12y - 2z + 20 = 0, then the coordinates of the other end of the diameter are

1. (4, 3, 5)
2. (4, 3, -3)
3. (4, 9, -3)
4. (4, -3, 3)

Correct answer: (4, 9, -3)

Solution

The center of the sphere can be found by rewriting the equation in standard form, which reveals that the center is at (3, 6, 1). The coordinates of the other end of the diameter can be determined by using the midpoint formula; since one end is (2, 3, 5), the other end must be (4, 9, -3) to maintain the center at (3, 6, 1).

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