Answer:
y = -5x + 7
Step-by-step explanation:
Segment bisector of the segments AB and CD will pass through the midpoint of these segments.
Midpoint of a segment is given by the coordinates = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
where, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme ends of the segments.
Coordinates of the midpoint of AB = [tex](\frac{6-4}{2},\frac{3+1}{2})[/tex]
= (1, 2)
Coordinates of the midpoint of CD = [tex](\frac{5-1}{2},\frac{-5-1}{2})[/tex]
= (2, -3)
Let the equation of the line will be,
[tex]y-y_1=m(x-x_1)[/tex]
Slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{2+3}{1-2}[/tex]
= -5
Therefore, equation of the line will be passing through (1, 2) and slope (-5),
y - 2 = (-5)(x - 1)
y = -5x + 5 + 2
y = -5x + 7
