Is the Diagram in My Geometry Homework Incorrect?

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SUMMARY

The discussion centers on a geometry homework problem where the student questions the accuracy of a diagram related to a mapping theorem. Specifically, the student notes that point X' is incorrectly positioned on segment P'X' instead of segment P'Q', contradicting the theorem's requirement that distances d(P,X) and d(P',X') be equal. The resolution emphasizes that the diagram serves merely as an illustration, and the correct positioning of X' is determined through calculations rather than visual representation.

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Homework Statement


On my attached pic "wtflang2," he says X' must lie on the segment between P' and Q', but the picture is not indicating that. X' seems to be on a segment P'X', not on segment P'Q'.Not only that, but he says d(P,X) and d(P',X') should be equal but his picture does not show this.

Homework Equations

The Attempt at a Solution


[/B]
He says the image of a line segment under F is a line segment. So if PQ is a line segment, and PX is a line segment contained within PQ, I don't understand how the mapping gives us a line segment P'X' that is not contained in line segment P'Q'.

Can anyone help me make sense of this theorem? I am utterly confused by it.
 

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X' is drawn elsewhere because "at that point in the text" you don't know where it is yet. After calculating the distances you learn that X' has to be on the line P'Q'. You could draw a revised diagram with that new knowledge. The calculations matter, the diagrams are just for illustration.
 
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