SOLUTION: The line 3x+2y=16 is the perpendicular bisector of the segment AB Find coordinates of point B given that a) A=(-1,3) (b) A=(0,3)
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Question 147044: The line 3x+2y=16 is the perpendicular bisector of the segment AB Find coordinates of point B given that a) A=(-1,3) (b) A=(0,3) Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website! 3x+2y=16
2y=-3x+16
y=-3x/2 + 8 The slope is -3/2
The slope of the line it bisects is the negative reciprocal of its slope, 2/3
If a=(-1,3):
y-y[1]=m(x-x[1])
y-3=2/3(x-(-1))
y-3=2x/3 + 2/3
y=2x/3 + 11/3
3x+2(2x/3 + 11/3)=16 substitute for y in the original equation
3x+4x/3 + 22/3=16
9x+4x+22=48 multiply each side by 3 to eliminate fractions.
13x=26
x=2
y=5
(2,5) The intersection of the 2 lines on the graph.
To go from(-1,3)to (2,5) x is increased by 3 and y by 2
If we take (2,5) and increase x by 3 and y by 2 we get (5,7) which is B (answer).
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You should be able to do part (b) now.
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Ed
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