A line segment is bisected by a line with the equation # 4 y + 3 x = 2 #. If one end of the line segment is at #( 2 , 1 )#, where is the other end?
One possible other end would be at
The equation of all possible answers is
If the given equation is to be the perpendicular bisector:
The distance from
If we wanted the equation for all solution values
Consider a line
Note the labeling of Line Segment
which we know from the previous work are in the ratio
Consider any other arbitrary Line Segment
Note again the labeling that divides
the ratio of
That is any arbitrary line segment connecting
its equation is
If we wanted
Consider the line
Since the slope of
the slope of
and the equation of
The endpoint of this perpendicular line segment can be derived as the intersection of
My apologies for the length of this solution.
If anyone can provide a complete solution more briefly, please post it.