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Question
Find the equations of the sides of the triangles the coordinates of whose angular point is respectively (1, 4), (2, −3) and (−1, −2).
Solution
Let the given points be A (1, 4), B (2, −3) and C (−1, −2).
Let \[m_1 , m_2 \text { and } m_3\] be the slopes of the sides AB, BC and CA, respectively.
\[\therefore m_1 = \frac{- 3 - 4}{2 - 1}, m_2 = \frac{- 2 + 3}{- 1 - 2} \text { and } m_3 = \frac{4 + 2}{1 + 1}\]
\[ \Rightarrow m_1 = - 7, m_2 = - \frac{1}{3} \text { and } m_3 = 3\]
So, the equations of the sides AB, BC and CA are
\[y - 4 = - 7\left( x - 1 \right), y + 3 = - \frac{1}{3}\left( x - 2 \right) \text { and } y + 2 = 3\left( x + 1 \right)\]
\[ \Rightarrow 7x + y = 11, x + 3y + 7 = 0\text { and } 3x - y + 1 = 0\]
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