How Can You Solve the Homework Challenge on Vectors and Similar Triangles?

AI Thread Summary
The discussion focuses on solving a homework problem involving vectors and similar triangles. A key point is the justification for stating that segment PQ is half the length of segment SR, which is based on Q being the midpoint of OR and the parallelism between PQ and SR. The similarity of triangles OPQ and OSR is emphasized, confirming that point P is the midpoint of OS. Additionally, there is a note on the correct notation for the triangles, advising against using the Δ symbol for the quadrilateral PQRS. Overall, the conversation provides insights into geometric relationships and proper notation in mathematical problems.
LiHJ
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Homework Statement



Dear Mentors and PF Helpers,

Here's the question:

image.jpg


Homework Equations

The Attempt at a Solution



Here's my solutions:

Please let me know whether I'm right. Thank you

image.jpg

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Hi LiHJ. How would you justify saying PQ is half the length of SR?

Edit: the rest looks right, though you are a bit rough & ready with the geometry. PQRS shouldn't be designated using the Δ symbol! :)
 
Because the question mention that Q is the midpoint of OR and PQ is parallel to SR. So triangle OPQ is similar to triangle OSR. Therefore P is a midpoint of OS
 
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Thank you;)
 

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