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Question
Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.
Solution
Let the given points be A (x, −1), B (2, 1) and C (4, 5).
Slope of AB = \[\frac{1 + 1}{2 - x} = \frac{2}{2 - x}\]
Slope of BC = \[\frac{5 - 1}{4 - 2} = \frac{4}{2} = 2\]
It is given that the points (x, −1), (2, 1) and (4, 5) are collinear.
\[\therefore\] Slope of AB = Slope of BC
\[\Rightarrow \frac{2}{2 - x} = 2\]
\[ \Rightarrow 1 = 2 - x\]
\[ \Rightarrow x = 1\]
Hence, the value of x is 1.
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