Given are the points $P (1,0)$ and $Q (3,2)$. The points $P$ and $Q$ have the same distance to a certain line $l$, which intersects the positive x-axis in the point $A$ and the positive y-axis in the point $B$. The area of the triangle $ABO$ is minimal. Get the equation of $l$.
What I did:
First of all, I got the equation of line $PQ$, which is: $y=x-1$.
Then I got the bisector of $PQ$, because every point on that line is equidistant to $P$ and $Q$. The bisector: $y=-x+3$.
However, this turned out to be wrong, and I had a gut feeling that it would be wrong, since I did nothing with the statement 'The area of triangle of $ABO$ is minimal', because I thought (and still think) that there is just 1 line equidistant from both points.. Can anyone help me with this?