Question 547180
You need 2 things:
1) slope of the line segment
2) (x,y) of the midpoint
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First you find the x-coordinate of the midpoint
(4,-7) and (7,-4)
{{{ ( 7 + 4 ) / 2 = 11/2 }}}
Now the y-coordinate
{{{ ( -4 + (-7) ) / 2  = -11/2 }}}
The midpoint is at (11/2, -11/2)
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Now find slope
slope = change in y / change in x
{{{ m = ( -4 -(-7) ) / ( 7 -(-7) ) }}}
{{{ m = 3 / 14 }}
Any line perpendicular to this line will have
a slope = {{{ -( 1/m ) = -( 1/(3/14)) }}}
{{{ -(1/m) = -14/3 }}}
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Now I can use the point-slope formula
{{{ -14/3 = ( y - (-11/2) ) / ( x - 11/2 ) }}}
{{{ -14/3 = ( y + 11/2) / ( x - 11/2 ) }}}
{{{ y + 11/2 = (-14/3)*( x - 11/2 ) }}}
{{{ y + 11/2 = (-14/3)*x + 154/6 }}}
Multiply both sides by {{{6}}}
{{{ 6y + 33 = -28x + 154 }}}
{{{ 6y = -28x + 121 }}}
{{{ y = -(14/3)*x + 121/6 }}} answer
check:
Does it go through (11/2, -11/2) ?
{{{ y = -(14/3)*x + 121/6 }}} 
{{{ -11/2 = -(14/3)*(11/2) + 121/6 }}} 
{{{ -33 = (-14)*11 + 121 }}}
{{{ -33 = -154 + 121 }}}
{{{ -33 = -33 }}}
OK
Here's a plot of the lines ( I don't know how to show a line segment,
so I show it a a continuous line
{{{ graph( 400, 400, -30, 30, -30, 30, (3/14)*x - 77/14, -(14/3)*x + 121/6 ) }}}