GMAT Math

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

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.

It is correct assuming you know that the two 'b' values are different.