SOLUTION: what is the equation of the perpendicular bisector of ag, where a (12,-1) and g(3,9)?

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Question 1207326: what is the equation of the perpendicular bisector of ag, where a (12,-1) and g(3,9)?
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
You can do this!

Find the midpoint of the two points using Mid Point formula.

Find slope of your two points using formula for slope.

Find the negative reciprocal of that slope. You use this along with the found midpoint; and you can use the point-slope formula for equation of a line....



You could find as a possible equation, 18x-20y=55, but choose whatever form you want.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

what is the equation of the perpendicular bisector of ag, where
a (12,-1) and g(3,9)?

the equation of the ag will have a slope
m=%289-%28-1%29%29%2F%283-12%29=-10%2F9
y-y%5B1%5D=+m%28x-x%5B1%5D%29....plug in slope and point g(3,9)
y-9=+-%2810%2F9%29%28x-3%29
y-9=+-%2810%2F9%29x-%28-%2810%2F9%293%29
y-9=+-%2810%2F9%29x%2B10%2F3
y=+-%2810%2F9%29x%2B10%2F3%2B9
y=+-%2810%2F9%29x%2B37%2F3

the equation of the perpendicular bisector will have a slope negative reciprocal to -10%2F9+and it is
m=-1%2F%28-10%2F9%29=9%2F10
bisector will pass through midpoint of ag which is (%2812%2B3%29%2F2, %28-1%2B9%29%2F2)=(15%2F2,4)
use slope - point form
y-y%5B1%5D=+m%28x-x%5B1%5D%29....plug in slope and point (15%2F2,4)
y-4=%289%2F10%29%28x-15%2F2%29
y-4=%289%2F10%29x-27%2F4
y=%289%2F10%29x-27%2F4%2B4
y=%289%2F10%29x-11%2F4+=> answer