skylimit wrote:
Line L and line K have slopes -2 and 1/2 respectively. If line L and line K intersect at (6,8), what is the distance between the x-intercept of line L and the y-intercept of line K?
A) 5
B) 10
C) \(5\sqrt{5}\)
D) 15
E)\(10\sqrt{5}\)
Source: GMAT Prep Now
Is there a nice fast solution?
Follow the posting guidelines.As for your question, "Is there a nice fast solution?", it is not going to be helpful either to you or any other member when you ask such questions without providing information as to what did you do to approach this question. It is fine to ask an "alternate method" but to talk about "fastest" or "easiest" is going to defeat the purpose of having a useful discussion.
The classic way is:
Assume the equations of the 2 lines, L and K as
y=-2x+a and
y=x/2 +b respectively
As both these lines pass through (6,8), substitute x=6 and y=8 to get the values of a and b as 20 and 5 respectively.
Thus equations of the 2 lines become
L: y=-2x+20, x-intercept = (10,0) and
K: y=x/2 +5, y-intercept = (0,5) respectively
Thus the distance = distance between (10,0) and (0,5) = \(\sqrt {(10-0)^2+(0-5)^2}\) = \(5\sqrt{5}\). C is the correct answer.