we know that
As the midpoint is a point on the perpendicular line, we can solve by eliminating the other equations, like this:
a) Check if the point (-1,-2) is on the line y=-4x-4:
for x=-1
y=-4*(-1)-4--------> y=0
0 is not -2--------> that is not the equation
b) Check if the point (-1,-2) is on the line y = −4x − 6:
for x=-1
y=-4*(-1)-6--------> y=-2
-2 is equal to -2--------> that is the equation
c) Check if the point (-1,-2) is on the line y = x – 4
for x=-1
y=-(-1)-4--------> y=-5
-5 is not -2--------> that is not the equation
d) Check if the point (-1,-2) is on the line y = x – 6
for x=-1
y=-(-1)-6--------> y=-7
-7 is not -2--------> that is not the equation
therefore
the answer is
y = −4x − 6:
