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 )

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)   (Show Source): You can put this solution on YOUR website!
Given line equation

and the intercepts on axes,
(0,-2) and (3,0).

You want the line with slope , and containing the point having the coordinates point (3/2,-1).
.
.
Answer by MathLover1(20849)   (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

x intercept:

=> A=(,)
y intercept:

=> B=(,)
slope of given line (also a segment AB) is

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
intersection of the line segment and a perpendicular bisector will be midpoint of the line segment which is
M(,)=(,)
the equation of a perpendicular bisector will be
....substitute and M=(,)

-> the equation of a perpendicular bisector

Answer by ikleyn(52781)   (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 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.

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