SOLUTION: its says determine the distance between point A(-1,-3) and point B(5,5). Write an Equation of the perpendicular bisector of side AB! and i have to use a grid

Algebra ->  Length-and-distance -> SOLUTION: its says determine the distance between point A(-1,-3) and point B(5,5). Write an Equation of the perpendicular bisector of side AB! and i have to use a grid      Log On


   

Question 356302: its says determine the distance between point A(-1,-3) and point B(5,5). Write an Equation of the perpendicular bisector of side AB! and i have to use a grid
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the distance formula,
D=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29
D=sqrt%28%285-%28-1%29%29%5E2%2B%285-%28-3%29%29%5E2%29
D=sqrt%28%285%2B1%29%5E2%2B%285%2B3%29%5E2%29
D=sqrt%28%286%29%5E2%2B%288%29%5E2%29
Finish the calculation to get the distance.
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Now find the slope using the two points.
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29=8%2F6=4%2F3
Perpendicular lines have slopes that are negative reciprocals.
m%5B1%5D%2Am%5B2%5D=-1
%284%2F3%29%2Am2=-1
m%5B2%5D=-3%2F4
Now you have the slope of the perpendicular bisector, you just need the midpoint of the first line.
Use the midpoint formula,
x%5Bm%5D=%28x%5B1%5D%2Bx%5B2%5D%29%2F2=%28-1%2B5%29%2F2=4%2F2=2
y%5Bm%5D=%28y%5B1%5D%2By%5B2%5D%29%2F2=%28-3%2B5%29%2F2=2%2F2=1
Now you have the slope and a point for the perpendicular bisector, use the point slope form of a line,
y-y%5Bp%5D=m%28x-x%5Bp%5D%29
y-1=-%283%2F4%29%28x-2%29
y-1=-%283%2F4%29x%2B3%2F2
y=-%283%2F4%29x%2B3%2F2%2B2%2F2
highlight%28y=-%284%2F3%29x%2B5%2F2%29
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