Mathematics - Straight Lines Question with Solution | TestHub

Let co-ordinates of $\mathrm{A}\left(x_1,x_1\right)$ and $\mathrm{B}\left(x_2,m{x}_2\right)$. Clearly ${\left(x_1-x_2\right)}^2+{\left(x_1-m{x}_2\right)}^2=16$. Let mid point be $\mathrm{P}(h,k)\Rightarrow x_1+x_2=2h$ and $x_1+m{x}_2=2k\Rightarrow {\left(x_1-x_2\right)}^2+4x_1{x}_2=4h^2$ and ${\left(x_1-m{x}_2\right)}^2+4m{x}_1{x}_2=4k^2$ $\Rightarrow {\left(x_1-x_2\right)}^2+{\left(x_1-m{x}_2\right)}^2=4h^2+4k^2=16$ when $m=-1$.