about to only mathematics

Options

A. (2,3)
B. `(2,3sqrt2)`
C. (0,3`sqrt2`)
D. none of these

Answer

C

Explanation

Let Q (`x_(1),y_(1)`) be the reflection of the point P(4,1)in the line mirror y=x-1. Then, the coordinates of Q are given by
`(x_(1)-4)/1=(y_(1)-1)/(-1)=(-2(4-1-1))/({1^(2)+(-1)^(2)})`
`rArr(x_(1)-4)/1=(y_(1)-1)/(-1)=-2rArrx_(1)=2,y_(1)=3`
Thus, the coordinates of Q are (2,3)
Now, Q is translated parallel to x-axis in the positive direction by 1 unit. So, the coordiantes of R aer (1+2,3) or (3,3) .
Suppose OR makes an angle `theta` with OX.Then,
`tan theta=(3)/(3)=1 implies theta=(pi)/(4)`
It is given that OR is rotated through `(pi)/(4)` in anticlockwise sense to coincide with OS. Therefore, OS makes a right angle with OX and OS =OR`=3sqrt(2)` .
Thus, the coordiantes of S are `(0,3sqrt(2))`.