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Question
Determine whether the given point is collinear.
\[P\left( 1, 2 \right), Q\left( 2, \frac{8}{5} \right), R\left( 3, \frac{6}{5} \right)\]
Solution
\[P\left( 1, 2 \right), Q\left( 2, \frac{8}{5} \right), R\left( 3, \frac{6}{5} \right)\]
Slope of PQ = \[\frac{\frac{8}{5} - 2}{2 - 1} = \frac{\frac{- 2}{5}}{1} = \frac{- 2}{5}\]
Slope of QR = \[\frac{\frac{6}{5} - \frac{8}{5}}{3 - 2} = \frac{\frac{- 2}{5}}{1} = \frac{- 2}{5}\]
So, the slope of PQ = slope of QR.
Point Q lies on both the lines.
Hence, the given points are collinear.
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