Question

PLEASE HELP! O is the centre of a sphere and has coordinates (2, -3,5). If AB is a diameter of the sphere

and A has coordinates (5, 1, 1), find the coordinates of B. Give your answer as an ordered
triple (x, y, z).

Answer 1

(-2, -6, -6)

Explanation:

The center of the sphere, O, and point A, are located on the same diameter of the sphere, AB. Thus, the line segment joining these two points is the radius of the sphere. Therefore, the length of the line segment, OA = OB = r, where r is the radius of the sphere.

We can find the length of the line segment, OA, using the distance formula:

√((5 - 2)^2 + (1 + 3)^2 + (1 - 5)^2) = √(3^2 + 4^2 + (-4)^2) = √49 = 7

Since OA = OB = 7, the coordinates of B can be found by subtracting the radius, 7, from the x, y, and z-coordinates of point A:

B = (5 - 7, 1 - 7, 1 - 7) = (-2, -6, -6)Therefore, the coordinates of B are (-2, -6, -6).