Question 1077948
A( 8,9 )
B( 1,7 )
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Points have the form ( x,y )
Find 1/3 of the x-distance from A to B
{{{ ( 8 - 1 )/3 = 7/3 }}}
{{{ 8 - 7/3 = 17/3 }}}
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Find 1/3 of the y-distance from A to B
{{{ ( 9 - 7 )/3 = 2/3 }}}
{{{ 9 - 2/3 = 25/3 }}}
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The factory should be at C ( 17/3 , 25/3 )
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check:
distance AC should be 1/2 of distance CB
{{{ sqrt(( 8 - 17/3 )^2 + ( 9 - 25/3 )^2 ) = (1/2)*sqrt(( 17/3 - 1 )^2 + ( 25/3 - 7 )^2 )
{{{ sqrt( 7/3 )^2 + ( 2/3 )^2 ) = (1/2)*sqrt( 14/3 )^2 + ( 4/3 )^2 )
Square both sides
{{{ ( 7/3 )^2 + ( 2/3 )^2 = ( 1/4 )*( ( 14/3 )^2 + ( 4/3 )^2 ) }}}
{{{ 49/9 + 4/9 = (1/4)*( 196/9 + 16/9 ) }}}
{{{ 196/9 + 16/9 = 196/9 + 16/9 }}}
That seems to prove it
Get another opinion definitely!