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Let $O$ be the origin $A (3, - 2), B (1, 2)$ and $C (1, 1)$ . The pair of points which are on different sides of the line $2 x + 3 y = 5$ are

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A, B

A, C

B, C

A, B ,C

answer is A.

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Detailed Solution

$2 x + 3 y - 5 = 0$

$A (3, - 2) B (1, 2) C (1, 1)$

$L_{11} = L_{(3, - 2)} = 6 - 6 - 5 < 0$

$L_{22} = L_{(1, 2) =} 2 + 6 - 5 > 0$

$L_{33} = L_{(1, 1) =} 2 + 3 - 5 = 0$

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