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Rotation of a point around a vertical axis

Statement. Rotate point A(6, 4, 2) by 90 degrees around the vertical axis through the origin.

Step-by-step solution

1. The axis is perpendicular to the horizontal plane, so in the plan it looks like a point (the origin).
2. The height does not change: the point rotates in a horizontal plane, so A stays at height 2.
3. In the plan, draw the radius OA and turn it 90 degrees with the compass, anticlockwise.
4. Raise the new position to height 2 to get A1 and A1''.

Result

A1(-4, 6, 2).

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