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Def1. Let L be a line in E. We define the "orthogonal projection onto L" to be

Ol = {(P,Q)| P,Q in E and either

1.P lies on L and P=Q or

2.Q is the foot of the perpendicular to L through P.

Problem 1. Let L be a line in E. Show that Ol is not a rigid motion because it fails condition (iii) of definition 1 and it fails conditions (i) and (ii) of definition 3

Def.1 part (iii) = If P and Q are elements of F, then the second coordinate of P is not the second coordinant of Q.

Def. 3 part (i) = If P is an element of E, then there is an element of F having P as its second coordinant

Def. 3 part (ii) = If (P,P') and (Q,Q') are two elements of F then the segment PQ and P'Q' are congruent.

2. Relevant equations

3. The attempt at a solution

I can prove that it fails Def 3 part ii because rigid motions preserve distances where orthogonal projections don't, but could use help on the other two.

Thanks

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# Homework Help: Orthogonal projection onto line L

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