A) 5
B) 9
C) 12
D) 4
Correct Answer: B
Solution :
Median through C is \[x=4\] So clearly the \[x\] coordinate of \[C\] is 4. So let \[C=(4,y),\] then the midpoint of \[A(1,2)\] and \[C(2,y)\] which is \[D\] lies on the median through \[B\] by definition. Clearly, \[D=(\frac{1+4}{2},\frac{2+y}{2})\]. Now, we have, \[\frac{3+4+y}{2}=5\Rightarrow y=3\]. So, \[C=(4,3)\]. The centroid of the triangle is the intersection of the medians. It is easy to see that the medians \[x=4\] and \[x+y=5\] Intersect at \[G=(4,1)\]. The area of triangle \[\Delta ABC=3\times \Delta AGC=3\times \frac{1}{2}\times 3\times 2=9\]. (In this case, it is easy as the points \[G\] and \[C\]lie on the same vertical line \[x=4\]. So the base \[GC=2\] and the altitude from \[A\] is \[3\] units.) So the answer is option B.You need to login to perform this action.
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