InterviewSolution
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InterviewSolution
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The point `(4,1)` undergoes the following two successive transformations (i) Reflection about the line `y=x` (ii) Translation through a distance 2 units along the positive X-axis. Then the final coordinate of the point areA. `(4,3)`B. `(3,4)`C. `(1,4)`D. `((7)/(2),(7)/(2))` |
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Answer» Correct Answer - B Let the reflection of `A(4,1)` in y=x is B (h,k). Now, mid -point of AB is `((4+h)/(2),(1+k)/(2))` which lies on y=x. i.e. `(4+h)/(2)=(1+k)/(2)rArrh-k=-3` .......(i) So, the slope of liney=xis 1. `therefore` Slope of `AB=(h-1)/(k-1)` `rArr 1.((h-4)/(k-4))=-1` `rArr h-4=1-k` `rArrh+k=5` and `h-k=-3` `2h=2rArrh=1` On putting h=1in Eq.(ii) we get `k=4` So, the point is `(1,4)` Hence, after translation the point is `(1+2,4)` or `(3,4)` |
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