Line given by a bi-section
Task number: 2351
Find the equation for a line \(\pi\), s.s. the segment between the Cartesian axes is split by the point \(A=(2{,}6)\) into two parts in ratio 1:2.
Resolution
By the similartity of triangles follows, that \(\pi\) intersects axes either in points \((3{,}0)\) and \((0{,}18)\) or in points \((6{,}0)\) and \((0{,}9)\). The first pair of intersections yields equation \(x/3+y/18-1=0\), the second \(x/6+y/9-1=0\).
Result
There are two possible solutions: \(\pi_1: 9x+y=18\), and \(\pi_2: 3x+2y=18\)
