Question

The image of the point $A(1,2)$ by the line mirror $y=x$ is the point $B$ and the image of $B$ by the line mirror $y=0$ is the point $(\alpha ,\beta )$. Find $\alpha$ and $\beta$ .

• A. $\alpha =1,\beta =2$
• B. $\alpha =2,\beta =-1$
• C. $\alpha =-2,\beta =1$
• D. $\alpha =-2,\beta =-1$

Answer 1

The correct option is B $\alpha =2,\beta =-1$

Let $B(h,k)$ be the image of $A(1,2)$ w.r.t the mirror $x-y=0$
$\Rightarrow \frac{h-1}{1}=\frac{k-2}{-1}=\frac{-2(-1)}{2}$
$\Rightarrow h-1=-k+2=1$
$\Rightarrow h=2,k=1$
So, the image of $A$ is $B(2,1)$
Let the image of $B(2,1)$ w.r.t the mirror $y=0$ be $C(\alpha ,\beta )$
$\Rightarrow \frac{\alpha -2}{0}=\frac{\beta -1}{1}=\frac{-2\left(1\right)}{1}$
$\Rightarrow \alpha =2,\beta =-1$