SOLUTION: The coordinates of points A and B are A(-2,-3) and B(2,-5). What is an equation of the line that is perpendicular to AB^ at its midpoint?

Algebra ->  Equations -> SOLUTION: The coordinates of points A and B are A(-2,-3) and B(2,-5). What is an equation of the line that is perpendicular to AB^ at its midpoint?      Log On


   

Question 905236: The coordinates of points A and B are A(-2,-3) and B(2,-5). What is an equation of the line that is perpendicular to AB^ at its midpoint?
Found 2 solutions by richwmiller, josgarithmetic:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
those points go though this line
y= -0.5x-4
y= 2x+b
is perpendicular
A(-2,-3) and B(2,-5)
y= 2x+b

5= 2*2+b
b=1
so the equation is y= 2x+1

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Find slope of the given points and find slope of the line perpendicular;
Find the midpoint of the given points;
Use either equation form you are comfortable with and form the equation for the perpendicular line
which contains the midpoint.

m%5Bg%5D=%28-3-%28-5%29%29%2F%28-2-2%29=2%2F%28-4%29=-1%2F2, "given".

m%5Bg%5D%2Am=-1, to ensure m is for the needed perpendicular line.

%28-1%2F2%29m=-1
highlight_green%28m=2%29

M:
x=%28-2%2B2%29%2F2=highlight_green%280%29;
y=%28-3-5%29%2F2=highlight_green%28-4%29.

You want the equation for the line with slope 2 and passing through point (0,-4).
The rest of this is not done, so that you will do it, finish.