A) \[(-1,\,\,3)\]
B) \[(1,\,\,3)\]
C) \[(3,-1)\]
D) \[(4,\,\,1)\]
Correct Answer: B
Solution :
Let the coordinates of a point are (x, y). We have, \[{{x}_{1}}=-1,\]\[{{y}_{1}}=7;\]\[{{x}_{2}}=4,\]\[{{y}_{2}}=-3\] and \[{{m}_{1}}=2,\]\[{{m}_{2}}=3\] \[\therefore \]By using section formula, \[=(8x+3)(5x+3)-40{{x}^{2}}=(39x+9)\,\,{{m}^{2}}\]\[=\frac{5}{5}=1\] and\[y=\frac{{{m}_{1}}{{y}_{2}}+{{m}_{2}}{{y}_{1}}}{{{m}_{1}}+{{m}_{2}}}=\frac{2\,\,(-3)+3(7)}{2+3}=\frac{-6+21}{5}\]\[=\frac{15}{5}=3\] Hence, coordinates of the point are (1, 3).
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