Question 184086
Find an equation y = mx + b of the perpendicular bisector of the line segment joining the points A(3,5) and B(9,-1).
;
Find the slope of the line given by the above coordinates; m = {{{(y2-y1)/(x2-x1)}}}
Assign the points as follows:
x1=3; y1=5
x2=9; y2=-1
m1 = {{{((-1-5))/((9-3))}}} = {{{(-6)/6}}} = -1 is the slope
:
Find the slope of the perpendicular line (m2)
m1*m2 = -1
-1*m2 = -1
m2 = {{{(-1)/(-1)}}}
m2 = +1 is the slope of the perpendicular line
:
Find the mid-point of the line mp = {{{(x2+x1)/2}}} & {{{(y2+y1)/2}}}
mp = {{{(9+3)/2}}} {{{(5-1)/2}}} = {{{(12)/2}}} & {{{4/2}}}
mid point: x=6 y=2, (we know  lines intersect at this point)
:
Find the perpendicular line using the point/slope equation y - y1 = m(x-x1)
and the intersection coordinates:
y - 2 = +1(x - 6)
y - 2 = x - 6
y = x - 6 + 2
y = x - 4; is the perpendicular line
:
The slope m is 1
The constant b is -4