Question 1014363
<pre>

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:

{{{(ay-bx)/p = (cx-az)/q = (bx-cy)/r}}}, we get 

{{{((2)(8)-(8)(3))/(10) = ((4)(3)-(2)(8))/(5) = ((8)(3)-(4)(8))/(10)}}}  

{{{(16-24)/(10) = (12-16)/(5) = (24-32)/(10)}}}

{{{(-8)/(10) = (-4)/(5) = (-8)/(10)}}}

{{{-4/5=-4/5=-4/5}}}, so {{{(ay-bx)/p = (cx-az)/q = (bx-cy)/r}}} is true.

However, look at what are supposed to be equal:

{{{x/a = 3/2}}}, {{{y/b=8/8 = 1}}}, and {{{z/c = 8/4 = 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</pre>