# A line segment is bisected by a line with the equation # 3 y + 5 x = 2 #. If one end of the line segment is at #( 5 , 8 )#, where is the other end?

##### 1 Answer

The other end is at

#### Explanation:

This problem is in the perpendicular bisectors so it is safe to assume that the bisected line is perpendicular; that means that its equation is of the form:

To find the value of c, substitute in the point

The equation of the bisected line is:

The given equation is:

Multiply equation [1] by -3 and equation [2] by 5

Add equations [3] and [4]:

Let

The x coordinate of the other end of the line segment is twice that change added to the starting x coordinate:

To find the y coordinate,

The other end is at