A line segment is bisected by a line with the equation # - 6 y + 2 x = 3 #. If one end of the line segment is at #( 4 , 8 )#, where is the other end?
1 Answer
Any point on the line
Explanation:
Consider a horizontal line segment from
The equation of the horizontal line segment from
Noting that
The intersection of this horizontal line segment with the given bisector line will occur at
Continuing to travel horizontally a point twice as far away from
will be at
That is
For any point which could be such an endpoint, a line through this point parallel to the bisecting line will provide all possible bisected line segment endpoints.
Using the previously determined possible endpoint
we can write the slope-point version:
Any solution to the equation
Here is a graph of the point and the two lines in question:
graph{(-6y+2x-3)(3y-x+27)((x-4)^2+(y-8)^2-0.02)=0 [-25.65, 25.64, -12.83, 12.81]}