Yes, that approach will put the points in the correct plane. However the approach that I suggested puts the points in the correct plane, and in the correct position, in one step. Better yet, it works even if the planes are parallel. And its higher dimensional analogs work in any number of dimensions.

In reply to Re^8: (OT) moving points from one plane to another by tilly
in thread (OT) moving points from one plane to another by merrymonk

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