Question

Indicate the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5).

Answer 1

The correct answer is x+3y=-3

Explanation:

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.

In the end, our answer will be x+3y=-3.

Answer 2

find th midopint

the mindpoint of 2 points (x1,y1) and (x2,y2) is
((x1+x2)/2,(y1+y2)/2)

so midpoint is ((4+2)/2,(1-5)/2)=(6/2,-4/2)=(3,-2)

now find the slope of the line
it is perpendicular to the line with (4,1) and (2,-5)
find the slope of th eline passing through (4,1) and (2,-5)
slope between (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)
so the slope between (4,1) and (2,-5) is
(-5-1)/(2-4)=-6/-2=3

perpendicular lines have slopes tha tmuliplty to get -1
3 times what=-1
what=-1/3


so what is the equation of a line that passes through the point (3,-2) and has a slope of -1/3

the equation of a line that has a slope of m and passes through (x1,y1) is
y-y1=m(x-x1)
so
y-(-2)=-1/3(x-3)
y+2=-1/3(x-3)
if we want slope intercept form
y+2=-1/3x+1
y=-1/3x-1

if we want standard form
1/3x+y=-1
x+3y=-3