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Variations on a Theme of Linear Measure

You may shift the red, yellow and black lines by dragging white points A, B and C, and rotate these lines around their white points, and so set the positions of invariant points X and Y.

The invariants may be sent as far out of view as is altogether possible, one at a time, or together, or they may be set in view, one at a time, or together. Please do note carefully that this requires rotation of lines, not translation.  Lines cannot translate.  (See a formal list of changes.)

Change the intervals by dragging D and/or U, and shift the entire set of them using the yellow point.