# 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 *locus* in which the point B can be located is