The equation of a line segment joint the two points A(0,a) and B(a,b) is given by y=−13x−2 Find the equation of the perpendicular bisector of AB in the form ax+by+c=0, where a, b and c are integers.
Give your answer in the form ax+by+c=0 with no spaces.
Answers
Answer:
46 - 46 - a is equal to 48 812
Given : The equation of a line segment joint the two points A(0,a) and B(a,b) is given by y=(−1/3)x−2
To Find : equation of the perpendicular bisector of AB in the form ax+by+c=0,
Solution:
y = -x/3 - 2
A = ( 0 , a)
=> a = 0 - 2
=> a = - 2
B = ( a , b)
=> b = -a/3 - 2
=> b = -(-2)/3 - 2
=> b = 2/3 - 2
=> b = -4/3
A = ( 0 , - 2)
B = ( - 2 , - 4/3)
Mid point = ( - 1 , -5/3 )
Slope of perpendicular bisector = 3
y - (-5/3) = 3 (x - (-1))
=> y + 5/3 = 3(x + 1)
=> 3y + 5 = 9 (x + 1)
=> 3y + 5 = 9x + 9
=> 9x - 3y + 4 = 0
9x - 3y + 4 = 0 is equation of the perpendicular bisector of AB
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