A line segment is bisected by a line with the equation # 7 y + x = 1 #. If one end of the line segment is at #(1 ,6 )#, where is the other end?
There would be any number of points which when joined with (1,6) that would make a line segment, bisected by 7y+x=1.
However if the line 7y+x=1 is a perpendicular bisector, the required point would be unique.
Hence considering 7y+x=1 as a perpendicular bisector, let (a,b) be the required point. The midpoint of the line segment joining (1,6) and (a,b) would be
Next, slope of line joining (1,6) and (a,b) is
Solving the two equations 7b+a=-41 and 7a-b=1, the result would be