UPSC NDA I 2021 Mathematics Solved Paper

Concept For knowing the equation of the line mirror its slope needs to be determined first. When two lines are perpendicular, the product of their slope is $-1 .$ If $m$ is the slope of a line, then the slope of a line perpendicular to it is $-\frac{1}{m}$. Theslope of a line passing through the distinct points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $m=\;\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}$ Equation of line is $(y-y_{1})=m(x-x_{1})$ Calculation: The line mirror is perpendicular to the line joining the two points. So, for the point, $x=\;\frac{4-4}{2}=0$ $y=\;\frac{2-2}{2}=0$ $(x,y)=(0,0)$ Slope of the line joining $(-4,2)$ and $(4,-2)=\;\frac{-2-2}{4-(-4)}=\;\frac{-1}{2}$ As the mirror is perpendicular to this line so, $m \times \left(\;\frac{-1}{2}\right) = -1$ $m=2$ Hence, the equation of line mirror is, $\;\frac{y-0}{x-0}=2$ $\therefore y=2x$