A) \[(1,4)\]
B) \[(1,-\,4)\]
C) \[(4,1)\]
D) \[\left( -\frac{1}{5},-\frac{22}{5} \right)\]
Correct Answer: D
Solution :
Let the reflection point of (3, 2) is\[P({{x}_{1}},{{y}_{1}})\] Equation of perpendicular line AB i.e., \[x+2y+1=0\]is ?.(i) \[2x-y+\lambda =0\] Since, it is passing through the point (3, 2) \[\Rightarrow \]\[6-2+\lambda =0\]\[\Rightarrow \]\[\lambda =-\,4\] \[\therefore \] \[2x-y-4=0\] It is also passes through the point \[({{x}_{1}},{{y}_{1}})\] \[2{{x}_{1}}-{{y}_{1}}-4=0\] ?(ii) Now, mid point of PQ is M \[\left( \frac{{{x}_{1}}+3}{2},\frac{{{y}_{1}}+2}{2} \right)\]it lies on the line AB. \[\Rightarrow \]\[\frac{{{x}_{1}}+3}{2}+2\left( \frac{{{y}_{1}}+2}{2} \right)+1=0\] [from (i)] \[\Rightarrow \] \[{{x}_{1}}+2{{y}_{1}}+9=0\] ?(iii) On solving Eqs. (ii) and (iii), we get \[{{x}_{1}}=-\frac{1}{5}\]and \[{{y}_{1}}=-\frac{22}{5}\]You need to login to perform this action.
You will be redirected in
3 sec