Find the equations of the straight lines which pass through the origin and trisect the portion of the straight line - Maths - Straight Lines

Question

Find the equations of the straight lines which pass through the
origin and trisect the portion of the straight line 2x+3y=6 which
is intercepted between the axes

ramandeep.singh · Accepted Answer

Let the equation of the line be

As P trisects the line AB, therefore, coordinates of P are $P = (\frac{2 (3) + 1 (0)}{2 + 1}, \frac{2 (0) + 1 (2)}{2 + 1}) = (2, \frac{2}{3})$ Similarly, Q also trisects the line AB Therefore, coordinates of Q are $Q = (\frac{1 (3) + 2 (0)}{2 + 1}, \frac{1 (0) + 2 (2)}{2 + 1}) = (1, \frac{4}{3})$ Thus, equation of line OP is given by $\frac{y - \frac{2}{3}}{0 - \frac{2}{3}} = \frac{x - 2}{0 - 2}$ âˆ´x - 3y = 0 (1) Equation of line OQ is given by $\frac{y - \frac{4}{3}}{0 - \frac{4}{3}} = \frac{x - 1}{0 - 1}$ âˆ´4x - 3y = 0 (2) Lines (1) and (2) pass through the origin and trisect the portion of the line 2x + 3y = 6

Find the equations of the straight lines which pass through the origin and trisect the portion of the straight line 2x+3y=6 which is intercepted between the axes