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
• D. x + 8y 9 = 0

Answer 1

The correct option is C

7x – y = 6

The required line is the line passing through the intersection of two lines and the image of the point on the line y = x and mirror 2x – y = 1.

∴ Given lines intersect at (1, 1)

Image of (0, 0) in the line mirror 2x – y = 1 is given by

$\frac{x-0}{2}=\frac{y-0}{-1}=-2\frac{(2x0-0-0-1)}{4+1}\Rightarrow x=\frac{4}{5},y=\frac{-2}{5}$

$\therefore$ Required line passes through (1,1) and $(\frac{4}{5},\frac{-2}{5})$. So its equation is

y-1 = $\frac{-\frac{2}{5}-1}{\frac{4}{5}-1}(x-1)\Rightarrow 7x-y=6$