SOLUTION: If {{{(ay-bx)/p = (cx-az)/q = (bx-cy)/r}}} then prove that {{{x/a =y/b=z/c}}}

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Question 1014363: If %28ay-bx%29%2Fp+=+%28cx-az%29%2Fq+=+%28bx-cy%29%2Fr then prove that x%2Fa+=y%2Fb=z%2Fc
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

It isn't true.  Here is a DISproof.  Let:

a=2, y=8, b=8, x=3, p=10, c=4, z=8, q=5, r=10

Substitute those values in:

%28ay-bx%29%2Fp+=+%28cx-az%29%2Fq+=+%28bx-cy%29%2Fr, we get 

  

%2816-24%29%2F%2810%29+=+%2812-16%29%2F%285%29+=+%2824-32%29%2F%2810%29

%28-8%29%2F%2810%29+=+%28-4%29%2F%285%29+=+%28-8%29%2F%2810%29

-4%2F5=-4%2F5=-4%2F5, so %28ay-bx%29%2Fp+=+%28cx-az%29%2Fq+=+%28bx-cy%29%2Fr is true.

However, look at what are supposed to be equal:

x%2Fa+=+3%2F2, y%2Fb=8%2F8+=+1, and z%2Fc+=+8%2F4+=+2

They aren't equal at all!  So we cannot prove what isn't true, can we?

Maybe there was something else given.  Check and see.

Edwin