gmatcraze wrote:
Can someone help to verify my approach to this problem? I agree that for DS problems, we need not solve it completely ... but am giving the steps below, in case this was a PS problem. Thanks.
What is the equation of the line that is perpendicular to line y=2x and passes through point (a, b)?
1. a = -b
2. a - b = 1
Sol.
Since the two lines are perpendicular, slope of given line =2
Slope of the perpendicular line = -1/2
To write the equation for the perpendicular line, we need the to find its y-intercept
From (1), Cannot determine the value of a and b. Not suff
From (2), Cannot determine the value of a and b. Not suff
From (1) and (2), -2b =1 => b=-1/2
Required equation of the line: y= -1/2x -1/2
I think that the answer is A.
According to the question, we are suppose to find the equation of the line that is perpendicular to the line y=2x. First of all, we already know that the slope of that line must be -1/2 because the product of 2 slopes that are perpendicular to each other is -1, since we already have 2, then the slope of the line that we're looking for is -1/2.
(1) a=-b, so if you substitute this to the given point (a,b), you will have (-b,b). Let's say that b is 5, so if b is positive, then we will have (-5,5) or if b is negative, then we'll have (5,-5). Either way doesn't matter because you can create the same line either way. So you can just pick your points with the slope of -1/2 and you can have your equation.
(2) doesn't tell us anything about the exact value of (a,b) because there are infinite posibilities such as (2,1) or even (100,99).
So my answer is A