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 are

Options

A. `(4,3)`
B. `(3,4)`
C. `(1,4)`
D. `((7)/(2),(7)/(2))`

Answer

B

Explanation

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)`