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