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In a $Δ A B C, A = (1, 2)$ . Mid–points of $A B, A C$ are respectively $(1, - 2), (2, 1)$ . Then $B, C$ are respectively

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$(1, - 6), (3, 0)$

$(1, - 6), (2, - 3)$

$(2, 0), (\frac{5}{2}, \frac{3}{2})$

$(- 5, 6), (0, 7)$

answer is A.

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Detailed Solution

$A (1, 2), F (1, - 2), E (2, 1)$

$\frac{A + B}{2} = F \Rightarrow B = 2 F - A$ $\Rightarrow (2, - 4) - (1, 2) = (1, - 6)$

$E = \frac{A + C}{2} \Rightarrow C = 2 E - A$ $= (4, 2) - (1, 2) = (3, 0)$

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