A) (1, 2)
B) (3, 4)
C) \[(-\text{ }1,0)\]
D) \[(-2,-1)\]
E) (2, 3)
Correct Answer: E
Solution :
Let\[Q(x,\text{ }y)\]be the image of the point\[P(4,\text{ 1})\]to the line\[y-x+1=0\]. Then, PQ is\[\bot \]to \[y-x+1=0\] \[\therefore \] \[\frac{y-1}{x-4}\times 1=-1\] \[\Rightarrow \] \[y-1=-x+4\] \[\Rightarrow \] \[y+1=4+1=5\] ...(i) And also midpoint of PQ i. e.,\[\left( \frac{4+x}{2},\frac{y+1}{2} \right)\] lies on \[y-x+1=0\] \[\therefore \] \[\frac{y+1}{2}-\frac{(4+x)}{2}+1=0\] \[\Rightarrow \] \[y+1-4-x+2=0\] \[\Rightarrow \] \[y-x-1=0\] \[\Rightarrow \] \[y-x=1\] ...(ii) On solving Eqs. (i) and (ii), we get \[y=3\] \[x=2\] \[\therefore \]Required point is (2, 3).You need to login to perform this action.
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