A) (2, 2)
B) (4, 5)
C) (3, 4)
D) (7, 7)
Correct Answer: D
Solution :
Mid-point of P(2,3) and Q(4,5) =(3,4) Slope of PQ=1 Slope of the line L=-l Mid-point (3,4) lies on the line L. Equation of line L, \[y-4=-1(x-3)\Rightarrow x+y-7=0\] ?(i) Let image of point R(0,0) be \[S({{x}_{1}},{{y}_{1}})\] Mid-point of\[RS=\left( \frac{{{x}_{1}}}{2},\frac{{{y}_{1}}}{2} \right)\] Mid-point \[\left( \frac{{{x}_{1}}}{2},\frac{{{y}_{1}}}{2} \right)\]lies on the line (i) \[\therefore \]\[{{x}_{1}}+{{y}_{1}}=14\] Slope of \[RS=\frac{{{y}_{1}}}{{{x}_{1}}}\] Since \[RS\bot \]line L \[\therefore \]\[\frac{{{y}_{1}}}{{{x}_{1}}}\times (-1)=-1\] \[\therefore \]\[{{x}_{1}}={{y}_{1}}\]From (ii) and (iii),\[{{x}_{1}}={{y}_{1}}=7\] Hence the image of R= (7,7)
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