A) \[(3,-10)\]
B) \[(-3,10)\]
C) \[(3,10)\]
D) \[(-3,-10)\]
Correct Answer: A
Solution :
[a] Let the coordinate of point A be \[({{x}_{1}},{{y}_{1}}).\] |
Centre C of a circle is the mid-point of AB. |
\[\therefore \] Mid-point of \[AB=\left( \frac{{{x}_{1}}+1}{2},\frac{{{y}_{1}}+4}{2} \right).\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,(2,-3)=\left( \frac{{{x}_{1}}+1}{2},\frac{{{y}_{1}}+4}{2} \right)\] |
On equating the x and y coordinates, we get |
3+\[2=\frac{{{x}_{1}}+1}{2}\] and \[-3=\frac{{{y}_{1}}+4}{2}\] |
\[\Rightarrow \,\,\,\,\,\,\,{{x}_{1}}=4-1\] and \[{{y}_{1}}=-6-4\] |
\[\Rightarrow \,\,\,\,\,\,\,{{x}_{1}}=3\] and \[{{y}_{1}}=-10\] |
Hence, coordinate of point A is \[(3,-10).\] |
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