# 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?

##### 2 Answers

Coordinates of the other end are

#### Explanation:

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

#### Explanation:

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.

Solving simultaneously:

We know for a line segment with coordinates

Midpoint coordinates:

Coordinates of end point of line segment:

Plot: