# A line segment is bisected by a line with the equation # 4 y - 2 x = 3 #. If one end of the line segment is at #( 5 , 6 )#, where is the other end?

##### 1 Answer

The other end of the line segment is at

#### Explanation:

First of all, the bisector of a line segment is perpendicular to the segment.

Perpendicular slope is the negative reciprocal of the original slope, so first step is to find the slope of the given line.

**Step 1: Finding the equation of the line segment**

Convert to slope-intercept form

Taking the negative reciprocal we have the slope of our line segment

NOTE: Because the bisector intersects the line segment at the midpoint, we can use the given point to find our

This gives us the equation of the line segment on infinite domain

**Step 2: Equate the two lines to find the intersection point at x**

Group x values together and factor

Sub in 6.1 to either equation to find y.

So our intersection point is at

**Step 3: Find the endpoint using the midpoint formula**

Because the intersection point

Substitute the original points at

**Answer**