The equation of the line AB is `y = x`. If A and B lie on the same side of the line mirror `2x-y = 1`, then the equation of the image of AB is (a) `x+y-2=0` (b) `8x+y-9=0` (c) `7x-y-6=0` (d) `None of these

Options

A. x+y=2
B. 8x+y=9
C. 7x-y=6
D. none of these

Answer

C

Explanation

We have to find the locus of the point (h,k) whose image on the line 2x-y-1 =0 lies on the line y=x. Now, the image of (h,k) on the line 2x-y-1=0 is given by
`(x_(2)-h)/(2) = (y_(2)-h)/(-1)=-(2(2h-k-1))/(5)`
`"or "x_(2) = (-3h+4k+4)/(5)`
`"and "y_(2) = (4h+3k-2)/(5)`
The point lies on y=x. Then,
`(-3h+4k+4)/(5) = (4h+3k-2)/(5) " or "7h-k=6`