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Rectangular Coordinate System in 3 Dimensions Points will be in form (x, y, z) dx=−y(()2 1 2 1 22 1 1 2 1 21 2 midpoint= , , 2 2 2 Example: Consider the region defined by 0 4≤x 1≤3≤y 2 3≤z Suppose we want to find the point closest to the origin. Choose x = 0, y = 1, z = 2. The point farthest from the origin is (4, 3, 3). Example: 2 5 x Consider the region defined by x−1 3y+x 2 3≤z Here, the y values are dependent upon the x value we choose. So if we want the point closest to the origin, we choose x = 2. That now makes y between 2-1 and 2+3 i.e. 1≤5≤y . So choose y = 1. Now choose z = 2. The closest point to the origin is (2, 1, 2).