A line segment is bisected by a line with the equation # -7 y + 3 x = 2 #. If one end of the line segment is at #( 2 , 4 )#, where is the other end?
1 Answer
Infinite solutions: any of the points in the line
Explanation:
First we should notice that the point (2,4) isn't in the line
But as the problem is stated it admits infinite solutions.
Calling AB the line segment with M the midpoint we have:
The orthogonal projection of A onto the line is also M when the segment is perpendicular bisected.
The slope of the line
So the slope of line perpendicular to the aforementioned is
And the equation of such a perpendicular line passing through A is
Combining the equations of the 2 lines
And
Finding B
So when the segment AB is perpendicularly bisected by the line mentioned in the problem
But since it is not required that the bisection happens perpendicularly the set of possible points B lays in a line parallel to the bisecting line and passing through