Question 1139062
A(-1,6)
B(5,4)
{{{ L[x] = (-1+5)/2)
{{{ L[x] = 2 }}}
and
{{{ L[y] = (6+4)/2 }}}
{{{ L[y] = 5 }}}
----------------------------
C(-5,-1)
D(3,-1)
{{{ M[x] = (-5+3)/2 }}}
{{{ M[x] = -1 }}}
and
{{{ M[y] = (-1+(-1))/2 }}}
{{{ M[y] = -1 }}}
---------------------------
The midpoints are:
L( 2,5)
M(-1,-1)
Use general point-slope formula
{{{ ( 5 -(-1) ) / ( 2 -(-1) ) = ( y -(-1) ) / ( x -(-1) ) }}}
{{{ 6/3 = ( y + 1 ) / ( x + 1 ) }}}
{{{ 2 = ( y + 1 ) / ( x + 1 ) }}}
{{{ y + 1 = 2*( x + 1 ) }}}
{{{ y + 1 = 2x + 2 }}}
{{{ y = 2x + 1 }}} answer
----------------------------
check:
A(-1,6)
B(5,4)
{{{ ( 6 - 4 )/( -1 - 5 ) = ( y - 4 ) / ( x - 5 ) }}}
{{{ 2/(-6) = (y-4)/(x-5) }}}
{{{ -1/3 = ( y-4 )/( x-5 ) }}}
{{{ -( x-5 ) = 3*( y - 4 ) }}}
{{{ -x + 5 = 3y - 12 }}}
{{{ 3y = -x + 17 }}}
{{{ y = (-1/3)*x + 17/3 }}}
and
C(-5,-1)
D(3,-1)
{{{ ( -1 -(-1) ) / ( -5 -(-3) ) = ( y -(-1) ) / ( x -(-3) ) }}}
{{{ ( -1 +1 ) / ( -2 ) = ( y + 1 ) / ( x + 3 ) }}}
{{{ ( y + 1 )/( x + 3 ) = 0 }}}
{{{ y + 1 = 0 }}}
{{{ y = -1 }}}
-----------------------
Here is a plot of the 3 lines:
{{{ graph( 400, 400, -10, 10, -10, 10, 2x + 1, (-1/3)*x + 17/3, -1 ) }}}