Answer:
[tex]y=\frac{5}{4}x+\frac{15}{4}[/tex]
Step-by-step explanation:
Coordinates of segment with endpoints J and K are,
J(-4, 9) and K(6, 1)
Midpoint of the segment JK = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
= [tex](\frac{-4+6}{2},\frac{9+1}{2})[/tex]
= (1, 5)
Slope of JK, [tex](m_1)=\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{9-1}{-4-6}[/tex]
= [tex]-\frac{4}{5}[/tex]
Let the equation of perpendicular bisector passing through [tex](x_1,y_1)[/tex] and slope [tex]m_2[/tex] is,
[tex]y-y_1=m_2(x - x_1)[/tex]
By the property of perpendicular lines,
[tex]m_1\times m_2=-1[/tex]
[tex]-\frac{4}{5}\times m_2=-1[/tex]
[tex]m_2=\frac{5}{4}[/tex]
Therefore, equation of the line passing through midpoint (1, 5) and slope = [tex]\frac{5}{4}[/tex] will be,
[tex]y-5=\frac{5}{4}(x-1)[/tex]
[tex]y=\frac{5}{4}x-\frac{5}{4}+5[/tex]
[tex]y=\frac{5}{4}x+\frac{15}{4}[/tex]
