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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.
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Solution
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
\[\frac{x}{\frac{- 32}{3}} + \frac{y}{\frac{24}{5}} = 1\]
\[ \Rightarrow 9x - 20y + 96 = 0\]
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