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Collinear Points

In the follow...

Question

In the following, find the value of ‘a’ for which the given points are collinear (2, 3), (4, a) and (6, – 3). (2 marks)

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Solution

$L e t t h e p o i n t s b e A (2, 3), B (4, a) a n d C (6, - 3) . S i n c e t h e g i v e n p o i n t s a r e c o l l i n e a r . A r e a o f a t r i a n g l e = 0 (0.5 m a r k) A r e a o f Δ A B C = \frac{1}{2} [(x_{1} y_{2} + x_{2} y_{3} + x_{3} y_{1}) - (x_{2} y_{1} + x_{3} y_{2} + x_{1} y_{3})] (0.5 m a r k) \frac{1}{2} [(2 a - 12 + 18) - (12 + 6 a - 6)] = 0 2 a + 6 - (6 + 6 a) = 0 2 a + 6 - 6 - 6 a = 0 - 4 a = 0 \Rightarrow a = 0 ∴ T h e v a l u e o f a = 0 (1 m a r k)$

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