What are the best places to put the two support poles


Problem:

Prove using analytic geometry

Here is the specific question:

A landscape architect is drawing plans for a rigid lightweight canopy to provide shade for a patio. Two poles will support the canopy. On the drawing, the coordinates of the verticies of the canopy are:

P (0,0)
Q ( 2,3)
R (8, -1)
and S (6, -4)

What are the best places to put the two support poles?

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Mathematics: What are the best places to put the two support poles
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