SOLUTION: Points A and B are the coordinates of the x and y intercepts of the line 2x-3y=6. Find the equation of a perpendicular bisector to the line segment □(→┬AB )

Algebra ->  Finance -> SOLUTION: Points A and B are the coordinates of the x and y intercepts of the line 2x-3y=6. Find the equation of a perpendicular bisector to the line segment □(→┬AB )      Log On


   

Question 1195341: Points A and B are the coordinates of the x and y intercepts of the line 2x-3y=6. Find the equation of a perpendicular bisector to the line segment □(→┬AB )
Found 3 solutions by josgarithmetic, MathLover1, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Given line equation 2x-3y=6
-3y=-2x%2B6
y=%282%2F3%29x-2
and the intercepts on axes,
(0,-2) and (3,0).

You want the line with slope -3%2F2, and containing the point having the coordinates point (3/2,-1).
.
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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Points A and B are the coordinates of the x and y intercepts of the line
2x-3y=6
x intercept:
2x-3%2A0=6
2x=6
x=3=> A=(3,0)
y intercept:
2%2A0-3y=6
-3y=6
y=6%2F-3
y=-2 => B=(0,-2)
slope of given line (also a segment AB) is m=%28-2-0%29%2F%280-3%29=-2%2F-3=2%2F3

the equation of a perpendicular bisector to the line segment □(→┬AB ) will have a slope negative reciprocal to the slope of given line
so, slope is m=-1%2F%282%2F3%29=-3%2F2
intersection of the line segment AB and a perpendicular bisector will be midpoint of the line segment AB which is
M(%283%2B0%29%2F2,%280-2%29%2F2)=(3%2F2,-1)
the equation of a perpendicular bisector will be
y-y%5B1%5D=m%28x-x%5B1%5D%29....substitute m=-3%2F2 and M=(3%2F2,-1)
y-%28-1%29=-%283%2F2%29%28x-3%2F2%29
y%2B1=-%283%2F2%29x-%283%2F2%29%28-3%2F2%29
y=-%283%2F2%29x%2B9%2F4-1
y=-%283%2F2%29x%2B5%2F4-> the equation of a perpendicular bisector




Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

I came to formulate the problem in a way as it SHOULD be done: 

    Points A and B are cross%28the%29 cross%28coordinates%29 cross%28of%29 the x and y intercepts of the line 2x-3y=6. 
    Find the equation of a perpendicular bisector to the line segment □(→┬AB )


Explanation :   points  ARE  NOT  coordinates - -

                    - in  Math,  points and coordinates are different subjects/notions/conceptions.