If the points (a, 1), (2, – 1) and are collinear, then a is equal to :

Engineering

Mathematics

Introduction to Determinants

Question

If the points (a, 1), (2, – 1) and $(\frac{1}{2}, 2)$ are collinear, then a is equal to :

$\frac{1}{4}$

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Slope of AB = slope of BC

\Rightarrow \frac{- 1 - 1}{2 - a} = \frac{2 - (- 1)}{\frac{1}{2} - 2}

\Rightarrow \frac{- 2}{2 - a} = \frac{3 \times 2}{- 3}

⇒ 6 = 12 – 6a

⇒ 6a = 6

a = 1

Hence, option A is correct answer.

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