How do I write the equation of the mirror line segment with endpoints (5,4) and (-1,-1)

Question

jdoe0001 · Answer

mirror in relation to what line or axis?

anonymous · Answer

it just says mirror line

aum · Answer

I think the endpoints, (5,4) and (-1, -1), are reflections of each other.  
So the mirror line will be the equation of the line passing through the midpoint and perpendicular to the line joining the endpoints.
Slope of the line joining the endpoints is: (4 - -1) / (5 - -1) = 5 / 6
Slope of the perpendicular line is: -6/5
Midpoint of  (5,4) and (-1, -1) is: ( (5-1)/2, (4-1)/2 ) = (2, 3/2)
Equation of the perpendicular line is: y = mx + b = -6/5x + b
It passes through the point (2, 3/2):  3/2 = -6/5 * 2 + b
3/2 + 12/5 = b
15/10 + 24/10 = b
39/10 = b

y = -6/5x + 39/10