Question

Find the equation of the line which passes through the point (− 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point. 

Answer 1

The x - coordinate of the point A is given by

\[- 4 = \frac{3 \times a + 5 \times 0}{3 + 5}\]

\[ \Rightarrow a = \frac{- 32}{3}\]

The y - coordinate of the point B is given by

\[3 = \frac{3 \times 0 + 5 \times b}{3 + 5}\]

\[ \Rightarrow b = \frac{24}{5}\]

The equation of the line passing is given by

\[\frac{x}{\frac{- 32}{3}} + \frac{y}{\frac{24}{5}} = 1\]

\[ \Rightarrow 9x - 20y + 96 = 0\]