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Question
By using the concept of equation of a line, prove that the three points (−2, −2), (8, 2) and (3, 0) are collinear.
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Solution
Let the given points be A (−2, −2), B (8, 2) and C (3, 0).
The equation of the line passing through A (−2, −2) and B (8, 2) is
\[y + 2 = \frac{2 + 2}{8 + 2}\left( x + 2 \right)\]
\[ \Rightarrow y + 2 = \frac{2}{5}\left( x + 2 \right)\]
\[ \Rightarrow 5y + 10 = 2x + 4\]
\[ \Rightarrow 2x - 5y - 6 = 0\]
Clearly, point C (3, 0) satisfies the equation \[2x - 5y - 6 = 0\]
Hence, the given points are collinear.
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