Question

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

Answer 1

mirror in relation to what line or axis?

Answer 2

it just says mirror line

Answer 3

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