A) \[2,2\]
B) \[2,3\]
C) \[3,2\]
D) \[5,2\]
Correct Answer: A
Solution :
| [a] Coordinates of mid-point of AB are \[\left( \frac{2a-2}{2},\frac{4+3b}{2} \right)\]i.e., \[\left( a-1,\frac{4+3b}{2} \right)\] |
| But\[M(1,2a+1)\]is the mid-point of AB. |
| (Given) |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,a-1=1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,a=2\] .(1) |
| and\[\frac{4+3b}{2}=2a+1\,\,\,\,\Rightarrow \,\,4+3b=4a+2\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,4+3b=4(2)+2\] [Using (1)] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,4+3b=10\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,b=\frac{10-4}{3}=\frac{6}{3}=2\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a=2,\,\,\,\,\,b=2\] |
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