Question 900532
The line {{{ x=4 }}} is a vertical line through (4,0)
The line segment trough the origin is {{{ a }}}
units long
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If I say that the intersection of the line segment
with {{{ x=4 }}} is ( 4,y ), then the distance 
between ( 0,0 ) and ( 4,y ) would be:
{{{ a^2 = ( 4 - 0 )^2 + ( y - 0 )^2 }}}
{{{ a^2 = 4^2 + y^2 }}}
{{{ y^2 = a^2 - 16 }}}
{{{ y = sqrt( a^2 - 16 ) }}}
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So, the coordinates of the other endpoint are:
( 4 , sqrt( a^2 - 16 ) )