The equation of the line segment AB is y=x. If A and B lie on the same side of the line mirror 2x-y=1, then the image of AB has the equation

Options

A. `y = (1)/(2) (x-1)`
B. `y = (x)/(2)`
C. `y = x - 1`
D. `2y = x +3`

Answer

B

Explanation

`/_ABC = tan theta = ((1)/(2)-1)/(1+(1)/(2)) =-(1)/(3) (m_(1) = (1)/(2),m_(2)=1)`
`:' AB = AC, :. /_ABC = /_ACB`

Hence, `-(1)/(3) = (m-1)/(1+m) rArr m =(1)/(2)` (here m is the gradient of line AC)
`:.` Equation of line AC is `y - 1 = (1)/(2) (x-2) rArr y =(x)/(2)`