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question about perpendicular bisector

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
Expert replies
by dhlee922 » Sun Mar 24, 2013 11:29 am
if you are told that there are 2 lines and one is the perpendicular bisector of the other, could you set the 2 lines equal to each other and solve for x and y and that would give you your midpoint?

y=mx+b
y= (-1/m)x+b

mx+b = (-1/m)x+b

is this basically saying this is where the lines intersect, therefore, this is the midpoint?

thanks
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Source: — Quantitative Reasoning |

by srcc25anu » Sun Mar 24, 2013 8:56 pm
That is not necessary.
for example lets say a line A passes through 1,5) and (5,1). slope of this line = -1. y intercept = 6. The equation of Line A line becomes y = -x +6 ---- A
Mid point of Line A = (3,3)
Slope of perpendicular line B = 1 (since m1 * m2 = -1)
y intercept = 0
therefore equation of line B becomes y = x --- B
so as we can see from the above example, we cannot assume the same y-intercept for a perpendicular bisector line. it could be same but not necessarily.
ideal way is to calculate the mid-point and we know tis mid-point will satisfy the equation of both the line and its perpendicular bisector.
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by Jim@StratusPrep » Mon Mar 25, 2013 5:38 am
It is correct assuming you know that the two 'b' values are different.
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