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isometry and angle bisector

1. Let A = ( root15, root 11), B= (root 11, - root15) C=(1,2) and D= ( 7,6). Is there an isometry that transform the segment AB onto segment CD? Explain.

Please see attached graph. I'm not sure of the answer.

2. Consider the following process for bisecting angle ABC: First mark M on BA and P on BC so that MB=PB, then mark new point N on BA and Q on BC so that NB = QB. Let E be the intersection of MQ and NP. Prove that segment BE is the desired angle bisector.

I can see it's the angle bisector on my graph.

Can I get some help writing a proof for it?