A) 2
B) 4
C) \[2\sqrt{2}\]
D) \[3\sqrt{2}\]
Correct Answer: C
Solution :
Let A = (p, q) and D = (1, 4) is the mid-point of BC. Slope of AD is - 2. \[\therefore \] \[\frac{4-q}{1-p}=-2\] \[\Rightarrow \] \[2p+q=6\] ?(i) Area of \[\Delta ABC\]\[=5\Rightarrow \,\left| \begin{matrix} p & q & 1 \\ -1 & 3 & 1 \\ 3 & 5 & 1 \\ \end{matrix} \right|=\pm \,10\] \[\Rightarrow \] \[-2p+4q-14=\pm 10\] \[\Rightarrow \] \[-p+2p-7=\pm \,5\] \[\Rightarrow \] \[p-2q=-2,\,\,-12\] ?(ii) \[\therefore \] \[(p,\,q)=(0,\,6),\,(2,\,\,2)\] \[\therefore \] \[OA=6,\,\,2\sqrt{2}\]You need to login to perform this action.
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