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If $Δ$ denotes the area of $Δ$ with vertices $(p + 1, 1), (2 p + 1, 3)$ and $(2 p + 2, 2 p)$ .
Match the items of column-1 with items of column-2 and choose the correct option.
Column - I Column - II
(A) p = 0 (1) $Δ = \frac{7}{2}$
(B) $p = \pm 1$ (2) $Δ = \frac{25}{2}$
(C) $p = 3$ (3) $Δ = \frac{3}{2}$
(D) $p = - 3$ (4) $Δ = 1$

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A→4, B→3, C→1, D→2

A→1, B→2, C→3, D→4

A→4, B→3, C→2, D→1

A→3, B→4, C→1, D→2

answer is A.

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Detailed Solution

$Δ = \frac{1}{2} | (p + 1) (3 - 2 p) + (2 p + 1) (2 p - 1) + (2 p + 2) (1 - 3) | = \frac{1}{2} | 2 p^{2} - 3 p - 2 |$

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