SOLUTION: Find an equation y = m x + b of the perpendicular bisector of the line segment joining the points A(3,5) and B(9,-1).
The slope m is
The constant b is
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Question 184086: Find an equation y = m x + b of the perpendicular bisector of the line segment joining the points A(3,5) and B(9,-1).
The slope m is
The constant b is
Found 2 solutions by solver91311, ankor@dixie-net.com:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
First thing to do is find the coordinates of the mid-point of line segment 
. That is because the perpendicular bisector of the line segment intersects the line segment at the mid-point by definition of a perpendicular bisector.
Use the mid-point formula:
 = \left(\frac{x_1 - x_2}{2},\frac{y_1 - y_2}{2}\right))
where )
and )
are the endpoints of the line segment.
Next you need the slope, m, of the line that contains the line segment:
where and are the endpoints of the line segment.
The slope of a perpendicular is the negative reciprocal of the slope of the given line, that is:
So, calculate 
using the value of the slope, m, determined above.
Then use this new slope value plus the fact that the calculated midpoint, )
is a point on the desired perpendicular to provide the given information for the point-slope form of the equation of a straight line, namely:
)
Make the appropriate substitutions for and m and then solve the equation for y in terms of x to obtain the desired slope-intercept form, 
The resulting 
and b will be the answers requested.
John
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 =
Assign the points as follows:
x1=3; y1=5
x2=9; y2=-1
m1 = = = -1 is the slope
:
Find the slope of the perpendicular line (m2)
m1*m2 = -1
-1*m2 = -1
m2 =
m2 = +1 is the slope of the perpendicular line
:
Find the mid-point of the line mp = &
mp = = &
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
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