Answer with Step-by-step explanation:
We are given that
P(-7,0) and Q(1,8)
We have to find the midpoint of PQ and write an equation of the line that passes through the midpoint.
Mid-point formula: [tex]x=\frac{x_1+x_2}{2}, y=\frac{y_1+y_2}{2}[/tex]
By using this formula ,
The mid point of PQ
[tex]x=\frac{-7+1}{2}=-3, y=\frac{0+8}{2}=4[/tex]
Hence, the midpoint of PQ is (-3,4).
Slope of PQ=[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{8-0}{1+7}=1[/tex]
Slope of perpendicular line=[tex]\frac{-1}{slope\;of PQ}=-1[/tex]
The equation of line which is passing through the point (-3,4) with slope -1 is given by
[tex]y-y_1=m(x-x_1)[/tex]
The equation of line which is passing through the point (-3,4) with slope -1 is given by
[tex]y-4=-1(x+3)[/tex]
[tex]y-4=-x-3[/tex]
[tex]y=-x-3+4[/tex]
[tex]y=-x+1[/tex]
