# A line segment is bisected by a line with the equation # 4 y - 6 x = 8 #. If one end of the line segment is at #( 1 , 8 )#, where is the other end?

##### 1 Answer

#### Explanation:

First rearrange

This will be perpendicular to the line through the point

We need to find the equation of this line. We know that if two lines are perpendicular then the product of their gradients is

Gradient of

Let

Then:

Using point slope form of a line and point

The intersection of

Substitute in

Co-ordinates of midpoint

The co-ordinates of the midpoint are given by:

So:

If the end points are

We have

Hence:

and

So other end point is: