A line segment is bisected by a line with the equation # -6 y - x = 3 #. If one end of the line segment is at #( 5 , 1 )#, where is the other end?
Coordinates of the other end are
Assumption : The line bisecting the segment is its perpendicular bisector.
Eqn of line
Slope of the line is -(1/6)#
Slope of altitude the line segment is 6
Eqn of line segment is
Solving Eqns (1) & (2) we get the intersection of the lines or the midpoint of the line segment.
Coordinates of mid point are
First we need to find the equation of the line that is perpendicular to the line
So second equation is:
The point of intersection of these lines is the coordinates of the midpoint of the line segment.
We know for a line segment with coordinates
Coordinates of end point of line segment: