My fist step to solving this question would be to find the mid-point of the given line. The mid point of (4,1) and (2,-5) is (3,-2). The mid point is where the perpendicular bisector connects or bisects the given segment. My second step would be to graph the two given points and to connect them, forming a line. This way, I would know the slope of the line and then I would be able to find the slope of the perpendicular bisector, since the slope for perpendicular lines is the opposite reciprocal of the given line. In doing this, I discovered that the slope of the segment with the given endpoints is 3 which means that the slope of the perpendicular bisector will be x
. So, so far we've got a point of intersection and a slope which is all we need to formulate the equation of the line that we are looking for.
What we know: line P endpoints (4,1) and (2,-5) (made up a line name for the this line) perpendicular lines' slope are opposite in sign and reciprocals of each other slope=m=(y2-y1)/(x2-x1) slope intercept for is y=mx+b
What we need to find: line Q (made this name up for this line) , a perpendicular bisector of the line p with given endpoints of (4,1) and (2,-5)
find slope of line P using (4,1) and (2,-5) m=(-5-1)/(2-4)=-6/-2=3
Line P has a slope of 3 that means Line Q has a slope of -1/3.
Now, since we are looking for a perpendicular bisector, I need to find the midpoint of line P to use to create line Q. I will use the midpoint formula using line P's endpoints (4,1) and (2,-5).
