Proving X, A, and Y Lie in a Straight Line | Triangle Medians Proof

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SUMMARY

The discussion focuses on proving that points X, A, and Y lie in a straight line when the medians BD and CE of triangle ABC are extended to points X and Y such that BD = DX and CE = EY. The proof employs indirect reasoning, suggesting that connecting points C and X, as well as B and Y, will yield a helpful geometric figure. A precise drawing is emphasized as a crucial tool for visualizing the relationships between these points.

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Jarvis Bull Dawg
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This is question I am really stuck with, please help if you can. (Its by indirect proof).
Question: The medians BD and CE in triangle ABC are produced to X and Y respectively so that BD = DX and CE = EY. Prove that X, A, and Y lie in a straight line.
 
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Here is what I have so far:
 

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No need in absurdum!

Connect C and X and see what helpful figure you are getting.
Same for B and Y.
Precise drawing would help.
 

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