Question 155114
Distance between two points:
http://www.purplemath.com/modules/distform.htm
{{{ d = sqrt((X2-X2)^2+(Y2-Y1)^2) }}}
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In your problem, it states:
{{{ AB=sqrt(34) }}}
This is the "distance" (d) between points A and B.
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Your two points:
A(2,9)
B(5,y)
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Plug the above into the distance formula:
{{{ d = sqrt((X2-X2)^2+(Y2-Y1)^2) }}}
{{{ sqrt(34) = sqrt((5-2)^2+(y-9)^2) }}}
squaring both sides we get:
{{{ 34 = (5-2)^2+(y-9)^2 }}}
{{{ 34 = 3^2+(y-9)^2 }}}
{{{ 34 = 9+(y-9)^2 }}}
{{{ 25 = (y-9)^2 }}}
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Taking the square root of both sides.  Here, notice that there are TWO different paths you can take -- sqrt(5) can equal -5 or +5.  If you chose the -5 route, y would NOT greater than 9.  Therefore, choose the +5 route:
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{{{ 5 = y-9 }}}
{{{ 14 = y }}}  (this is your answer)
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Reference: If we had taken the -5 route, you would have gotten:
{{{ -5 = y-9 }}}
{{{ 4 = y }}} 
y is NOT >9 -- toss out solution.