Question 124881
FIRST YOU NEED TO FIND THE SLOPE THROUGH (-8,8) & (6,1).
SLOPE=(1-8)/(6+8)=-7/14=-1/2.
THE EQUATION FOR THIS IS:
1=-6/2+b
1=-3+b
b=1+3
b=4 WHICH IS THE Y INTERCEPT
THUS THE EQUATION IS:
Y=-X/2+4 (RED LINE)
USING THE LINE FORMULA Y=mX+b & USING THE Y VALUE=-6 & THE SLOPE OF 2 (THE NEGATIVE RECIPRICAL OF -1/2) WHICH IS THE PERPENDICULAR LINE WHICH BISECTS ( 2 THE MID POINT) THE LINE BETWEEN (-8,8) & (6,1)WHICH IS
(8-1)/2=7/2=3.5+1=4.5 FOR THE Y VALUE
(6+8)/2=14/2=7-8=-1 FOR THE X VALUE. 
SO WE HAVE A SLOPE=2, A Y VALUE=4.5 & AN X VALUE=-1 WE SOLVE THE LINE FORMULA FOR b.
4.5=2*-1+b
4.5=-2+b
b=4.5+2
b=6.5
THUS THE LINE EQUATION IS:
Y=2X+6.5 (GREEN LINE)
NOW TO FIND THE X COORDINATE ASSOCIASTED WIT A Y VALUE=-6 WE SUBSTITUTE -6 FOR Y & SOLVE FOR X
-6=2X+6.5
2X=-6-6.5
2X=-12.5
X=-12.5/X 
X=-6.25 IS THE X COORDINATE OR (-6.25,6) FOR THE POINT EQUIDISTANCE FROM THE END POINT A (-8,8) & (6,1)
PROOF:{{{ graph( 300, 300, -10, 10, -10, 10, y = -x/2 +4, y = 2x +6.5) }}} (graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions y = -x/2 +4 and y = 2x +6.5).