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?
The other end of the line segment is at
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