Is the Diagram in My Geometry Homework Incorrect?

[r0bHadz]

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

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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.

 

[mfb]

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.