Question

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
A. x + y - 2 = 0
B. 8x + y - 9 = 0
C. 7x - y - 6 = 0
D. none of these

Answer 1

The required line is the line passing through the intersection of two lines and the image of a point on the line y = x in the line mirror 2x - y =1
Given lines intersect at (1,1)
The image of (0,0) in the mirror 2x - y = 1 is given by
`(x - 0)/(2) = (y-0)/(-1) -2 ((2 xx 0 -0-0 -1)/(4+ 1))`
`implies x = (4)/(5) , y = (-2)/(5)`
Thus , the required line passing through (1,1) and `((4)/(5) , (-2)/(5))`
So , its equation is
`y - 1 = ((-2)/(5) - 1)/((4)/(5) - 1) (x - 1)`
`implies y - 1 = 7 (x -1) implies 7x - y - 6 = 0`