Line up vertices (arbitrary plane)

Another n00b question coming up: how can I align a set of vertices to some arbitrary plane? For example if the plane was the global XY or YZ I would just select them all and scale them numerically (on one axis) to 0. However these are the vertices I want to be lined up diagonally:

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it’s probably not the answer you are looking for…but what about rotation the vertices you wish to align into horizontal or verticle position, remember the angle, and then scale them down to 0, and finally rotate those vertices back?

…i don’t know another way to align the vertices on an arbitrary angle.

How about changing the transform orientation to Normal? (It’s usually defaulted to Global, but there are also options for Local, Normal, and View). It should give you an axis that is close to what you want.
You could also play around with the Rotation/Scaling pivot. Choose Active Object if you want to use the axis of a face, vertex or edge as the reference point.

Use the Smooth button in the Editing (F9) Panel (see attached thumbnail) . Just select the two middle verts and push smooth a few times - make sure the “limit” value is set to 0.000 -
and the selected verts will converge to form your desired plane .

EDIT - you can also get the “smooth” function from pressing “W” - It’s on the list of options - it’s just “SMOOTH” NOT “Set Smooth” - they are two completely different things “smooth” works on geomtery “set smooth” is for display/ rendering calculations .

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Thanks for the replies. I finally did it by rotating and then scaling globally as was suggested. A bit of work but the other suggestions didn’t seem to do it right. Setting the cursor to a vertex position (shift+s) and using the cursor as the rotation & scaling origin comes in useful.