What is the path of the point (x,y) as the painting falls?

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SUMMARY

The discussion centers on the mathematical modeling of the path of a point (x,y) as an 8-foot-tall painting falls from a leaning position against a wall. Participants analyze the geometry involved, noting that the painting's height and the angles formed during its descent are crucial for deriving the correct equation. The confusion arises from the representation of the points and the dimensions involved, particularly the incorrect placement of the point (2,6) in relation to the painting's fall. Clear definitions of the variables and a proper diagram are essential for solving the problem accurately.

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Homework Statement



An art museum worker leaves an 8-foot-tall painting leaning against a wall. Later, the top of that painting slides down the wall, and the painting falls to the floor. Use the diagram to find an equation of the path of the point (x,y) as the painting falls.

Homework Equations



-None-

The Attempt at a Solution



All work is shown in the picture, but I am not sure if it is right or wrong...

http://tinypic.com/r/1tq2pf/5

It shows (0,y), (0,x) and shows that the painting is 6ft tall plus 2ft tall...

I still don't quite understand why and how the answer comes down to this...
 
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Your picture is impossible. The point (2,6) cannot possibly be on the ladder as you have pictured. The little upper triangle has both hypotenuse = 2 and leg = 2 as you have the picture drawn.

You haven't stated the problem clearly either. What does (x,y) represent in the first place?
 

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