The slope of CD is
[tex]m = \dfrac{6 - -4}{2 - 0} = 5[/tex]
The slope of the perpendicular bisector is the negative reciprocal,
[tex]n = -1/m = - \dfrac 1 5[/tex]
The perpendicular bisector passes through M, the midpoint of CD
M =( (0+2)/2, (-4 + 6)/2) = (1, -1)
So point slope form for the perpendicular bisector is
[tex]y - -1 = - \frac 1 5(x - 1)[/tex]
Solving for y gives slope intercept form.
[tex]y = - \frac 1 5 x - \frac 4 5[/tex]
Not sure how to type that without spaces; we didn't have online homework back then.
Answer: y=(-1/5)x-4/5
