Question 73157
Find the midpoint
*[invoke Midpoint_of_segment_connecting_two_point -2, 0, 2, 8]
So the perpendicular line is going to bisect the given segment at the midpoint. Now we must find the slope of the segment
{{{m=(y[2]-y[1])/(x[2]-x[1])}}}
{{{m=(8-0)/(2-(-2))}}}
{{{m=8/4}}}
{{{m=2}}}
Since a bisected line has a perpendicular bisector, we need a perpendicular slope. So the perpendicular slope is the negative reciprocal of the slope of the given segment
{{{m[p]=-1/m}}}where {{{m[p]}}} is the perpendicular slope
{{{m[p]=-1/2}}}
Now use the point-slope formula to find the equation
{{{y-y[1]=m(x-x[1])}}}
{{{y-4=(-1/2)(x-0)}}}Plug in m=-1/2 and (0,4)(the midpoint of the segment)
{{{y-4+4=(-1/2)x}}}Add 4 to both sides
{{{y=(-1/2)x+4}}}This is the line that bisects the segment
Note: you can use winplot (http://math.exeter.edu/rparris/winplot.html) to graph both the line and segment to see if it bisects.