- Given that
- the point \(A\) has coordinates \(( 4,2 )\)
- the point \(B\) has coordinates \(( 15,7 )\)
- the line \(l _ { 1 }\) passes through \(A\) and \(B\)
- find an equation for \(l _ { 1 }\), giving your answer in the form \(p x + q y + r = 0\) where \(p , q\) and \(r\) are integers to be found.
The line \(l _ { 2 }\) passes through \(A\) and is parallel to the \(x\)-axis.
The point \(C\) lies on \(l _ { 2 }\) so that the length of \(B C\) is \(5 \sqrt { 5 }\)
Find both possible pairs of coordinates of the point \(C\).Hence find the minimum possible area of triangle \(A B C\).