the point C lies on the perpendicular bisector of the line joining the points A (4,6) and B (10,2). C also LIES PARALLEL TO AB through (3,11)
1.Find the equation of the perpendicular bisector of AB
2.calculate THE COORDINATES OF C
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Answers
Equation of the perpendicular bisector of AB 2y = 3x - 13 , THE COORDINATES OF C (9, 7)
Step-by-step explanation:
A (4,6) and B (10,2)
Slope of AB = (2 - 6)/(10 - 4) = -4/6 = -2/3
Slope of Perpendicular to AB = 3/2
y = 3x/2 + c
Mid point of AB = (4 + 10)/2 , ( 6 + 2)/2 = 7 , 4
4 = 3(7/2) + c
=> 8 = 21 + 2c
=> c = -13/2
y = 3x/2 - 13/2
=> 2y = 3x - 13
equation of the perpendicular bisector of AB 2y = 3x - 13
Line Parallel to AB
y = -2x/3 + c
Passes throough (3 , 11)
=> 11 = - 2(3)/3 + c
=> c = 13
=> y = -2x/3 + 13
=> 3y = -2x + 39
=> 2x + 3y = 39
2x + 3y = 39
3x - 2y = 13
2*Eq1 + 3*eq2
=> 13x = 117
=> x = 9
y = 7
THE COORDINATES OF C (9, 7)
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