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

Algebra ->  Functions -> 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       Log On


   

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) About Me  (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:



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) About Me  (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 = %28y2-y1%29%2F%28x2-x1%29
Assign the points as follows:
x1=3; y1=5
x2=9; y2=-1
m1 = %28%28-1-5%29%29%2F%28%289-3%29%29 = %28-6%29%2F6 = -1 is the slope
:
Find the slope of the perpendicular line (m2)
m1*m2 = -1
-1*m2 = -1
m2 = %28-1%29%2F%28-1%29
m2 = +1 is the slope of the perpendicular line
:
Find the mid-point of the line mp = %28x2%2Bx1%29%2F2 & %28y2%2By1%29%2F2
mp = %289%2B3%29%2F2 %285-1%29%2F2 = %2812%29%2F2 & 4%2F2
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