Shifting of Axes

Q. Equation of the image of the pair of rays y = | x | by the line x = 1 is

1. | y | = x + 2
2. | y | + 2 = x
3. y = | x - 2|
4. none of these

Q.

If origin is shifted to the point $(2,3)$ without rotation of axes then the coordinates of the point $P$ which divides the join of $A(4,8)$ and $B(7,14)$ in the ratio $1:2$ or $2:1$ with respect to the new system of coordinates can be

1. $(2,5)$

2. $(3,7)$

3. $(4,9)$

4. $(5,11)$

Q. A'B' is the result of translation of AB by 2 units to the right and 6 units up. The new coordinates of B' after translation are .

1. (2, 10)
2. (4, 8)
3. (2, 8)
4. (4, 10)