# A line segment is bisected by a line with the equation # 2 y + 3 x = 3 #. If one end of the line segment is at #( 1 , 8 )#, where is the other end?

##### 1 Answer

To other end is at the point

#### Explanation:

The equation of any line segment that has the line,

, as its perpendicular bisector will have the standard form:

To find the value of C for the specified line segment, substitute the point

And then solve for C:

The equation of the bisected line segment is:

We shall use equations [1] and [2] to find the x coordinate of the point of intersection,

Multiply equation [1] by 3 and equation [2] by 2:

Add equation [3] to equation [4]:

The change in x (

The x coordinate of the other end,

where

To find the corresponding y coordinate,

To other end is at the point

Here is a graph with the two lines and the start and end points plotted: