# A line segment is bisected by line with the equation # 6 y - 7 x = 3 #. If one end of the line segment is at #(4 ,2 )#, where is the other end?

##### 1 Answer

#### Explanation:

First we note that if two lines are perpendicular then the product of their gradients is

We need to find the equation of a line that contains the point

Rearranging

If the gradient for our given line be

Using point slope form of a line:

Finding the point of intersection.

Solve

Substituting in

The coordinates for the midpoint of a line is given by:

Therefore:

Hence:

Coordinates of the other end are:

PLOT: