Line L and line K have slopes -2 and 1/2 respectively. If line L and l

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.