I'm really stumped on this question, but I'm sure the answer is really simple!

"There exist two lines and . A line passing through a pt A intersects these lines at the pts P and Q, respectively. The distance AQ is twice that of AP. What are the co-ordinates of P and Q?"

So far, I have said:

.

So,

.

If we denote the coordinates of P as and those of Q, , then by Pythagoras' Theorem,

and .

We can therefore substitute these two equations into to give an equation in and . Then, using the equations of the lines we can see that we can rewrite as

and as

which we can then use to derive an equation in terms of and . But how to eliminate one of these variables eludes me! Your help is much appreciated.